cations ^^^p

NATL INST. OF STAND & TECH

in O NBS TECHNICAL NOTE 1159

U.S. DEPARTMENT OF COMMERCE/National Bureau of Standards

A Fast Response,

Low-Frequency

Sampling Voltmeter
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards' was established by an act ot Congress on March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology

and facilitate their effective application for public benefit. To this end, the Bureau conducts

research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau's technical work is per- formed by the National Measurement Laboratory, the National Engineering Laboratory, and

the Institute for Computer Sciences and Technology.

THE NATIONAL MEASUREMENT LABORATORY provides the national system of

physical and chemical and materials measurement; coordinates the system with measurement

systems of other nations and furnishes essential services leading to accurate and uniform

physical and chemical measurement throughout the Nation's scientific community, industry,

and commerce; conducts materials research leading to improved methods of measurement,

standards, and data on the properties of materials needed by industry, commerce, educational

institutions, and Government; provides advisory and research services to other Government

agencies; develops, produces, and distributes Standard Reference Materials; and provides

calibration services. The Laboratory consists of the following centers:

Absolute Physical Quantities^ — Radiation Research — Chemical Physics —

Analytical Chemistry — Materials Science

THE NATIONAL ENGINEERING LABORATORY provides technology and technical ser- vices to the public and private sectors to address national needs and to solve national problems; conducts research in engineering and applied science in support of these efforts; builds and maintains competence in the necessary disciplines required to carry out this research and technical service; develops engineering data and measurement capabilities;

provides engineering measurement traceability services; develops test methods and proposes

engineering standards and code changes; develops and proposes new engineering practices;

and develops and improves mechanisms to transfer results of its research to the ultimate user. The Laboratory consists of the following centers:

Applied Mathematics — Electronics and Electrical Engineering^ — Manufacturing

Engineering — Building Technology — Fire Research — Chemical Engineering^

THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts

research and provides scientific and technical services to aid Federal agencies in the selection, acquisition, application, and use of computer technology to improve effectiveness and

economy in Government operations in accordance with Public Law 89-306 (40 U.S.C. 759), relevant Executive Orders, and other directives; carries out this mission by managing the Federal Information Processing Standards Program, developing Federal ADP standards

guidelines, and managing Federal participation in ADP voluntary standardization activities; provides scientific and technological advisory services and assistance to Federal agencies; and

provides the technical foundation for computer-related policies of the Federal Government.

The Institute consists of the following centers:

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'Headquarters and Laboratories at Gailhersburg, MD, unless otherwise noted; mailing address Washington, DC 20234. 'Some divisions within the center are located at Boulder, CO 80303.
JIATIONAL BUREAU

OF STANDAAOS

LIBRARY SEP 1 5 1982

A Fast Response, Low-Frequency ^^"^f"^

Sampling Voltmeter c^ ^^

' .o<r)S3

Barry A. Bell

Bruce F. Field

Thomas H. Kibalo

Center for Electronics and Electrical Engineering

National Engineering Laboratory

National Bureau of Standards

Washington, DC 20234

Sponsored in part by the DC and Low Frequency Engineering Subgroup of the

Calibration Coordination Group (CCG) of the Department of Defense.

="»eAU 0*

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige. Secretary

NATIONAL BUREAU OF STANDARDS. Ernest Ambler. Director

Issued August 1982
National Bureau of Standards Technical Note 1159

Natl. Bur. Stand. (U.S.), Tech. Note 1159, 113 pages (Aug. 1982)

CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1982

For Sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402.

Price (Add 25 percent for other than U.S. mailing.)
TABLE OF CONTENTS

Page

LIST OF FIGURES v

LIST OF TABLES vi

Abstract 1

1 . INTRODUCTION 1 1.1 Background 1 1.2 Low-Frequency Sampling Voltmeter Specifications 2

2. THEORY OF OPERATION 3

2.1 Instrument Architecture 3

2.2 Measurement Algorithms 5 2.2.1 Approximate Period 8

2.2.2 Exact Period 11

2.2.3 RMS Value 16

2.2.4 Harmonic Distortion 21

3. CIRCUIT DESCRIPTION 24

3.1 Microcomputer Board 27

3.2 Sampling Rate Generator 27

3.3 A/D Converter 28

3.4 Program Memory 29

3.5 Preamplifier 29

3.6 Front Panel Numerical Display/LEDs 30

3.7 Front Panel Switches 31

4. OPERATING INSTRUCTIONS 31 4.1 Installation 31 4.2 Controls 31 4.2.1 Power Switch 31 4.2.2 RMS AC + DC, RMS AC, Freq., Dist 31 4.2.3 10 mV, 100 mV, 1 V, 10 V Pushbuttons 32

4.2.4 Autoranging 32

4.2.5 Reset 32

4.3 Indicators 32

4.3.1 Reset 32

4.3.2 Display 32

4.3.3 Overload 32

4.3.4 RMS AC + DC, RMS AC, Freq., Dist 33

4.3.5 Front Panel Numerical Display 33

4.3.6 10 mV, 100 mV, 1 V, 10 V Ranges 33

4.4 Signal Input 33

m
TABLE OF CONTENTS (cont.)

Page

5. ERROR ANALYSIS 33

5.1 RMS Zero and Gain Error 33

5.2 Quantization Error 37

5.3 A/D Converter Nonlinearity Errors 40

5.4 Timing Errors 43

6. INSTRUMENT PERFORMANCE 45

6.1 Frequency (or, Period) Tests 45

6.2 RMS Voltage Tests 48

6.3 Harmonic Distortion Tests 53

7. CONCLUSIONS 53

8. REFERENCES 60

APPENDIX A - CALIBRATION PROCEDURES 62

APPENDIX B - MAINTENANCE AND TROUBLESHOOTING 64

APPENDIX C - SCHEMATICS 66

APPENDIX D - PHOTOGRAPHS 72

APPENDIX E - PARTS LIST 80

APPENDIX F - FLOWCHARTS OF CERTAIN MAJOR SUBROUTINES 88

IV
LIST OF FIGURES

Page

Figure 1. Simplified diagram of the voltmeter 4

Figure 2. Time sequence of the measurement process 6

Figure 3. Flowchart of measurement software 7

Figure 4. Approximate period detection 9

Figure 5. Approximate period detection at the signal peak .... 10

Figure 6. Plot of the error function , 13

Figure 7. Plot of the error function showing the shift of

the undesired minimum due to phase shift of the

signal 14

Figure 8. Plot of the error function showing the shift of

the undesired minimum as indistinguishable from

the true minimum 15

Figure 9. Real and imaginary components of the DFT 23

Figure 10. Measured error of the A/D converter before

adjustment of the gain and offset errors 35

Figure 11. Linearity plots from data converter test set.

Module 1 41

Figure 12. Linearity plots from data converter test set.

Module 2 42

Figure 13. Plot of error data comparing the LF Sampling Voltmeter

to the NBS AC Voltmeter/Calibrator (10 V range) .... 54

Figure 14. Plot of error data comparing the LF Sampling Voltmeter

to the NBS AC Voltmeter/Calibrator (1 V range) .... 55

Figure 15. Plot of error data comparing the LF Sampling Voltmeter

to the NBS AC Voltmeter/Calibrator (100 mV range) ... 56

Figure 16. Plot of error data comparing the LF Sampling Voltmeter

to the NBS AC Voltmeter/Calibrator (10 mV range) ... 57

Figure 17. An example of a distorted sine wave (4.7 percent third

harmonic distortion) with a dc offset produced by the

waveform generator 58
LIST OF TABLES

Page

Table 1. Backplane wiring diagram 25

Table 2. Final gain and offset errors after adjustment

of the A/D converter 34

Table 3. Calibration data for the frequency function of the

LF Sampling Voltmeter using an 0.01 percent accurate

Tektronix 505A frequency counter (in the period

measuring mode) 46

Table 4. Frequency test on engineering model 47

Table 5. Calibration of the rms ac + dc function of the voltmeter

by the Data Precision 2540A1 voltmeter at 20 Hz using

the waveform generator 49

Table 6. AC rms tests of prototype LF Sampling Voltmeter 50

Table 7. Tests of the LF Sampling Voltmeter (with preamplifier),

using the NBS AC Voltage Calibrator Standard 51

VI
A FAST RESPONSE, LOW-FREQUENCY SAMPLING VOLTMETER

Barry A. Bell, Bruce F. Field,* and Thomas H. Kibalo**

A low-frequency voltmeter utilizing a sampling technique

implemented with microprocessor-based electronics has been

developed to perform as a true rms ac voltmeter and distortion

analyzer. The instrument makes measurements accurate to

±0.1 percent (of reading) of the fundamental frequency, total

harmonic distortion, and true rms voltage of approximately

sinusoidal inputs from 2 mV to 10 V and frequencies from 0.1 to

120 Hz. A major feature of this instrument is the special

window crossing and error function algorithms which provide a software means for completing a measurement within two signal

periods at frequencies below 10 Hz.

Key words: algorithm; converter; distortion; microcomputer;

rms value; sampling; signal period.

1. INTRODUCTION

1 .1 Background

For many years the accurate measurement of the true rms value of

ac voltage has been of considerable interest to the National Bureau

of Standards. With the use of high accuracy thermal voltage converters,

whose ac-dc difference characteristics have been well established,

absolute measurement of ac voltage can be determined from 0.5 to

1000 V to an accuracy of 50 ppm or better over a frequency range

from 20 Hz to 100 kHz [1-3].

More recent investigations by the Electrosystems Division at NBS

have emphasized the extension of this capability to lower frequency

and voltage levels of interest in order to support the design,

calibration, and maintenance of vibration transducers (accelerometeramplifier systems). These transducers typically operate with

approximately sinusoidal signals having levels from a few millivolts

up to several volts and frequencies from tenths to tens of hertz. An

accurate ac voltmeter/calibrator, employing a multi-junction thermal

converter device for rms-to-dc conversion, has been developed at NBS

which is capable of making rms ac voltage measurements from 0.1 to

50 Hz at 2 mV to 10 V levels with ±0.1 percent accuracy (percent

Current NBS affiliation: Center for Absolute Physical Quantities,

National Measurement Laboratory.

Presently with Honeywell, Inc., Signal Analysis Center, Defense

Division, Annapolis, MD 21404

Numbers in brackets refer to the literature references listed at the

end of this report.

1
of reading) above 0.5 Hz and 5 mV and ±0.2 percent below these

values [4], Using the built-in calibrator, ac transfer measurements

(comparing ac input voltages with the ac calibrator) can be made to

an accuracy of ±0.02 percent. This instrument serves as the standard

in a calibration service now provided by NBS for ac voltmeters and

calibrators at frequencies from 0.1 to 10 Hz [5].

1.2 Low-Frequency Sampling Voltmeter Specifications

A new instrument has been developed using sampling techniques

which is capable of measuring the true rms voltage of approximately

sinusoidal waveforms from 2 mV to 10 V with frequencies between

0.1 to 120 Hz [6]. Although similar in its coverage of voltage and

frequency ranges as the earlier thermal converter-based standard,

this instrument is designed to have a very short response time as well as providing measurements of the rms value of the ac component

(only) of the input signal, the fundamental frequency, and the harmonic

distortion of the signal, which are features not available on the

thermal converter-based instrument.

A research and development program at NBS has been concerned with

developing and testing improved vibration accelerometers [7,8]. The

major motivation for improved accelerometers has been due to interest

in accurately predicting the mean-time-between-failure and failure

modes of equipment subjected to mechanical vibration. At present,

the largest source of uncertainty in calibrating these accelerometers

has been in the low-frequency voltage measurements. Also, studies

performed to evaluate new accelerometer designs have produced

inconclusive results because of the voltage measurement uncertainties.

The instrument described herein was developed to fulfill the following

requirements of vibration accelerometer calibration systems:

(1) Frequency range - 0.1 to 120 Hz (fundamental).

(2) Input voltage range - 2 mV to 10 V (4 1/2 decades).

(3) Accuracy - ±0.1 percent of reading (2a).

(4) The instrument should be an easy-to-use portable instrument

requi ring minimal calibration.

(5) Fast response time is desired, i.e., the measurement should

require no more than two periods at the lowest frequency.

(6) Capability of measuring total harmonic distortion of the

waveform for at least the first 10 harmonics.

It should also be noted that in many cases vibration accelerometers

produce slowly drifting dc offsets which are added to the ac component.

It is awkward to manually compensate for a changing offset; thus, it

is necessary that the instrument provide for measuring the ac component

(only) of the signal . 2
2. THEORY OF OPERATION

2,1 Instrument Architecture

Traditional measurement methods for ac waveforms all rely on some square law device (thermal converter, log amplifier, etc.) to provide

a true rms indication. For this application squaring modules based

on log amplifiers do not provide sufficient accuracies at low

frequencies. Thermal converters generally have large time constants

(of order 1-5 sec) due to the thermal mass of the heater and thermoelement

RMS to dc converters require large time constants for ripple filtering,

causing slow response to input voltage level changes. Although

improvements in thermal converter time constants can be made, increased

ac ripple on the dc output results, requiring additional filtering

or smoothing. Thus, if optimized for low-frequency measurements,

the response time of such an instrument becomes excessively large.

In addition, these methods do not provide any means for measuring

the distortion in the waveform.

The general approach taken for this low-frequency voltmeter is to

utilize a microcomputer for implementing as many functions as possible

with software, including timing and control of the input sampling

hardware. A simplified block diagram of the entire instrument is

shown in figure 1. A conventional sample-and-hold (S/H) amplifier

and successive approximation type of analog-to-digital (A/D) converter

are used for digitizing the input signal. The digital values are then

transferred to a microcomputer for calculation of the desired results.

The preamplifier (NBS 722 79184A) is a differential input amplifier

with programmable gain provided by external gain setting resistors

that can be changed by the microcomputer. Four^decade gain settings

are available to accommodate the wide range of possible input signals.

A data acquisition channel consisting of a S/H amplifier, a second

instrumentation amplifier, and an A/D converter are physically

contained in one hybrid module (NBS 722 79141 A). This second amplifier

is normally hardwired to provide only one of three input voltage ranges

for the A/D converter: 2.5, 5, or 10 V. However, external relays

have been added to allow the range to be set by the microcomputer.

Thus, a total of 12 gain settings is possible using combinations

of preamplifier gain and A/D range settings. All these settings are necessary in order to obtain adequate resolution for all specified

inputs. The A/D converter has 12-bit (11 bits plus sign bit)

resolution with a conversion time of 12 ysec.

The memory, timing, and control section (NBS 722 79094B) has two

functions. The first is a hardware clock that may be programmed by

the microcomputer to output a pulse at regular intervals. This pulse

is used to trigger the A/D converter to make a conversion; thus, a series of A/D readings uniformly spaced in time are generated

irrespective of the operation of the microcomputer which may be busy

with other calculations. The second function of this section is to
CMCM

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route control signals generated by the microcomputer to the gain

controlling relays for the preamplifier and the data acquisition module.

2 The microcomputer used is a National Semiconductor IMP-16C. This

is a 16-bit word length multi-chip microcomputer. It was chosen

mainly for the powerful arithmetic instructions in its instruction set.

All peripheral devices (display, A/D converter, etc.) are treated as memory locations and the instruction program (2048 16-bit words)

is stored in ultraviolet-erasable programmable read-only-memories

(EPROMS). A small amount of random access memory (RAM) is provided

on the microcomputer board for temporary storage of input values and

program variables.

2.2 Measurement Algorithms

Several kinds of algorithms are used to implement the voltmeter's

rms value, frequency (or period), and harmonic distortion functions.

Beyond the discussion given here, a more complete description of the

signal model for vibration accelerometer systems and associated

measurement algorithms is provided in [11].

Because the algorithms for calculating rms value require that the

value for the period be accurately determined, it is desirable to

have an initial sampling sequence which will adjust the signal level

so that it is within the range of the data acquisition preamplifier

system and, then, to determine the approximate period. Figure 2

shows the time sequence of the measurement process used within this

instrument.

During the first cycle (T]), sampling is begun at any arbitrary

point after the preamplifier gain has possibly been adjusted for

off-scale readings. Samples of the waveform are taken and an approximate

period is established. In order to measure the period more exactly,

and to obtain a set of samples with which to determine the rms value,

the sample rate clock (used to trigger the A/D converter) is then set

at 128 times the approximate frequency f

q (the reciprocal of the

approximate period). Any necessary adjustments to the gain settings

in the sampling hardware are made, a set of 147 samples is taken

during the second cycle (T2), and the corresponding A/D converter

readings stored. Depending on the setting of the function switches

on the front panel of the voltmeter, the rms value, frequency, or harmonic distortion is calculated during time T3, and the display

is updated with the new value. The whole process is then immediately

repeated. Figure 3 shows an overall flowchart of the measurement

software that corresponds to the measurement process just described.

2Certain commercial equipment, instruments, or materials are identified

in this paper in order to adequately specify the experimental results.

In no case does such identification imply recommendation or endorsement

by the National Bureau of Standards, nor does it imply that the material

or equipment identified is necessarily the best available for the purpose,

5
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cuCJc

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CD
(POWER ON )

RMS

CALCULATE RMS

READ SWITCH INPUTS

SET FRONT PANEL LEDS

INITIALIZE PERIPHERALS

AND VARIABLES

I SI PASS TO DETERMINE

PERIOD APPROXIMATELY

SET A/D CONVERTER RANGE

SAMPLE SIGNAL M? TIMES

CALCULATE PERIOD EXACTLY

FROM 147 SAMPLES

FREQUENCY

CALCULATE FREQUENCY

I UPDATE DISPLAY

ERROR-ADJUST PREAMPGAIN

RESET PUSHBUTTON ACTIVATED

7K

"9

DISTORTION

CALCULATE DISTORTION

Figure 3. Flowchart of measurement software.

7
2.2.1 Approximate Period

When starting a measurement of an unknown input waveform, the

frequency may be as low as 0.1 Hz or as high as 120 Hz. Sampling

at a fast enough rate to capture a 120 Hz signal would produce an excessive number of samples (to store in memory) of a 0.1 Hz signal.

A preliminary decision, based on the slope of the signal at the

start of the measurement sequence (T-|), determines whether a fast

(8 kHz) or slow {500 Hz) sampling rate is used.

With the sampling rate set at 500 Hz (see fig. 4, approximate

period detection), an initial reading is taken and temporarily stored

in the IMP-16C'sRAM. A higher and lower threshold value is calculated

at ±0.5 V with respect to this initial reading (upper bound of

±10 V). Thus, an initial "window" of sample values is established

as shown in figure 4. Sampling continues with each value tested

against the higher and lower threshold until either of these window

limits is exceeded. A count is made of the number of samples, N,

taken within the window. If the number of samples between the initial

value and a threshold is greater than five (N >5), it is assumed that

the frequency of the input signal is 1 Hz or less. In this case,

sampling continues at 500 Hz until a second window crossing occurs.

However, if the number of samples between the initial value and a threshold is less than five (N <5), it is assumed that the input

frequency is 10 Hz or greater. To obtain adequate resolution of the

period in this case, the sample rate clock is set to 8 kHz and the

measurement sequence restarted.

For frequencies less than 1 Hz, the first set of measurements is

thus used as an initial voltage window which defines the beginning of one signal period. Sampling continues until a new sample falls within

the window values. The next N samples are then saved and tested to

see if at least N/4 of them are within the window. If this condition

is met, it is assumed that the waveform has passed through the first

window crossing (see fig. 4). After the waveform is sampled further

and the second window crossing is found, one signal period has then

elapsed. The sampling rate clock is then set for 128 times the

approximate frequency (the reciprocal of the approximate period).

One problem which must be accounted for with this method is where

the window includes a peak on the waveform (see fig. 5). Since the

window of values will occur only once more in the period, waiting for

two window crossings would include two signal periods. To eliminate

this problem, if the initial window does occur over a signal peak,

the initial value is modified to start at the peak sample value with

a corresponding adjustment of the threshold value. Thus, the beginning

of the second window crossing is, again, the peak value which gives

an approximate measure of one signal period.
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Initial titndOM 1st window crossing

2nd window crossing

Problem: Initial window starts near a peak

start of measurement

Start of window

1st window crossing

2nd window crossing

Solution: Modify window to start at the pealt

Figure 5. Approximate period detection at the signal peak,

10
If during the sampling process of finding the initial window of

data values the upper bound of ±10 V is exceeded, overrange has

occurred and the preamplifier gain is immediately reduced. Once the

search is on for two more window crossings, however, autoranging

occurs differently, depending on the sampling rate. For 500 Hz

sampling, it is possible to check each reading for an overrange

condition and reset the preamplifier and A/D converter gains in realtime, i.e., between individual samples. When sampling at 8 kHz,

overrange tests are deferred until the end of one signal period. If

at this time it is determined that the input was overrange during the

measurement sequence, the gains are adjusted and the measurement

restarted.

2.2.2 Exact Period

As shown in figure 2, once the approximate frequency f has

been determined and the sample rate clock set to 128 x fg, the input

waveform is then sampled over a second cycle and the readings stored

for subsequent use in calculating the exact period, rms value, or harmonic distortion (refer also to fig. 3). In order to calculate

the rms value of the input signal, the period must be known with

approximately the same accuracy as is desired in the rms value [11].

As indicated by time T3 in figure 2 and the main program flowchart in

figure 3, 147 samples are taken in order to calculate the exact

period. The reason for storing more than the nominal 128 sample

values is to take the effects of noise and possible frequency modulation

(FM) into account.

An autocorrelation technique is used to determine the maximum

point of correlation with respect to the true signal period and the

beginning and endpoint samples taken of the waveform. This correlation

is accomplished by evaluating an error function that consists of

summing the difference in values of samples taken at approximately

corresponding times in the cycle:

n error function = Zi=l

Ei - Ei+N

where N = variable number of samples in period (125, 126, 127,

128, 129, 130, and 131)

Ei = sample values at beginning of cycle

and E^+i^ = corresponding sample values at beginning of next cycle

n = number of difference values summed; 16 points chosen,

based on empirical testing.

11
If the period was exactly an integral number of samples and the input

signal was free of noise or FM, this sum would go to zero for some value of N. However, since this probably is not the case, N is

varied as indicated above until a minimum value for the error function

is found. The set of seven error functions calculated is then

16 error function 1 = i i=l

^i ^i+125

16

error function 2 = z i=l

^i ^i+126

16 error function 3 = z 1=1 ^i " ^i+127

16

error function 4 = z i=l

^i+128

16 error function 5 = z i=l

^i " ^i+129

16

error function 6 = z i=l

'i+130

16

error function 7 = z i=l

^i ^i+131

Figure 6 shows a plot of a typical error function E^,

n E. = Z

^ i=l

^i - ^i.A

where A = correlation parameter, delta

a 10-point summation was used (n = 10) with samplinc

perioa contained exactly 360 samples.

Only begun for

A = 0. For this example, the

As is apparent from figure 6, a second unwanted minimum occurs for

this error function at approximately A = 170. The exact location

of this second minimum depends on the starting angle, however, as indicated in figure 7. As the starting angle approaches 90°, the

second minimum shifts very close to the true minimum, and it becomes

difficult to distinguish between the two (see fig. 8).

12
<n

00

cvi

ERROR FUNCTION

DEGREE STPRTING ANGLE

10 POINT SUM

180 240

DELTfi

Figure 6. Plot of the error functi on,

13
en

03

CM

ERROR FUNCTION

45 DEGREE STORTING PNGLE

10 POINT SUM

180 240

DELTR

Figure 7. Plot of the error function showing the shift of

the undesired minimum due to phase shift of the

signal .

14
CO

ERROR FUNCTION

90 DEGREE STPRTING ONGLE

10 POINT SUM

180 240

DELTR

Figure 8. Plot of the error function showing the shift of

the undesired minimum as indistinguishable from

the true minimum.

15
Therefore, to provide more resolution than integral values of N will allow, the two smallest sums of the error functions 1 through 7,

above, are used to linearly interpolate to the minimum point between

them (corresponding to A = 360). Experiment has shown that this

two-point interpolation provides the required ±0.1 percent accuracy

in the resultant value obtained for the exact period.

2.2.3 RMS Value

As stated in section 2.2.2, in order to calculate the rms value

of the input signal, the period must be known with approximately the

same accuracy as is desired in the rms value. To demonstrate this,

let the input signal E(t) be represented as

E(t) = cos t (rms value = _L )

Assume that the period T is determined incorrectly, i.e.,

T' = T (1-e)

where T = true period (27t in this case)

T' = measured period

e = fractional error .

Calculating the rms value directly as defined.

Erms =\t' / ^°^^^ "^^

Evaluating the integral Int,

T' Int = J

cosh dt = I' + ^^|il

16
or, substituting for T',

Tnf - T(T-0 + sin 2T (1-e)

iriL 2 ^ 4

For small e ,

sin 2T(l-e) = - 2Te

and

I^t , T(l-£) _ Te = T(l-2£)

2 2 2

Then ,

.2 = M _ _J T(l-2£)

rms T' T(l-e) * 2

^ 1 (1-2e)

^ 2 (1-e)

Again, for small e ,

1 1-e

Therefore,

c 1+e.

2 ^ i (l-2£)(l+£) ^ 1 (l-2£+e-2e2)

rms - 2 2

1 (1-e)

2

or ,

^.s = Vi(i-' = ^? Vi-=

17
But, for small e,

1/2 . yj-T^ = (1-e)'^" = l-E/2

and, therefore.

rms .VTV^ i (1-£/2)

/2

Assuming no other errors, the accuracy required for a period measurement

is one half the accuracy required for the rms value.

By definition, the rms value of a periodic waveform E(t) is

given by

= V 1 / [E(t: ^rms ^ ^ T J

tE(t)]^ dt , T e period .

Although other methods are possible, calculating the rms value directly

by means of numerical integration does not require an exact integral

number of samples per period, and the calculation is unaffected by

frequency modulation. Computer simulations have shown that numerical

integration by the midpoint method provides good reproducibility for

the value of the integral when measuring a signal with 100 samples/period

and a signal-to-noise ratio of 30dB [11]. For midpoint integration.

/f(t) dt - Z f(tk) At = ^ Z f(tk)

I<=1 ^ k=l

where a, b = limits of sample points

N = number of sample points

18
t|^ = k (b-a) + a k = 1, ..., N

N

For this particular implementation, 128 samples are nominally involved,

and

/[E(t)]2 dt . 1|M ^f [E(t^)]2

k=l

or.

Vr ^ ' -'

128

Calculation of Erms involves finding the square root of a 32-bit binary

number. An efficient algorithm for this purpose was used [12], and

developed into an assembly language program. The execution time is

approximately 27 ms. Also, when the exact period does not contain an integral number of samples, a small end correction is applied.

Because of the need to provide for measuring the ac component only of

the input signal , let

E(t) = Eq + A cos t (o) = 2Trf = 1)

T

where Eq = dc offset = J E(t)dt

A = peak amplitude of ac input with period, T = 27r

Then,

[E(t)]2 = Eq^ + 2EoA cos t + a2 cos2t

19
and

/ [E(t)]2dt = / Eo^dt + / 2EoA cos t dt

^^cos^ t dt

= Eo2[t]

T rT

" ^^°^ /'cos t dt

+ a2 / cos2 t dt

2 T

= Eo^T + + A"^ y .

Hence,

Ev,mr.(ac only)

rms -^

_A_ iVJ[E(t)]2 dt - e/

or, by numerical integration.

E^^^(ac only)

rms

^ -^

A.

128

T

^ tE(tk)]'

k=l

128

2 E(t,^)

k=l

20
2.2.4 Harmonic Distortion

When the percent of distortion function switch is selected, the

total harmonic distortion of the input signal is calculated during

T3 (see fig. 2).

The data samples from the second cycle (T2) are used to calculate

the coefficients of the Discrete Fourier Transform (DFT) of the input

signals by means of a 64-point "decimation-in-time" Fast Fourier

Transform (FFT) [9,11], Using the FFT algorithm, the dc, fundamental,

and 30 harmonic components of the input signal are obtained. Although

for some applications the measurement of the individual coefficients

is required, usually the total harmonic distortion (THD) as a figureof-merit is often most desired, or a measure of spectral purity.

THD is obtained by squaring and summing the coefficients of the

30 harmonics, and dividing this sum by the sum of the squares of the

harmonics plus the fundamental. This result is then multiplied by

100 and displayed as a percentage on the front panel. As specified

by the definition of THD, the dc component of the input signal is

not included in either of the sums.

In order to determine the coefficients of the fundamental and

30 harmonics of the input signal, the FFT algorithm requires the

multiplication of the data samples by a so-called "twiddle" factor,

W'" = e"^Ks)

where N = total number of samples

m = frequency index .

This factor is convenient since the DFT of the input signal x(t) is

given by

N-1 -j27TmfnT

X(mf) = A(mf) = Z x(nT.)e

n=0

where 00 = 27rmf = tj^

s

T^ = sampling time interval

m = 0, 1 ,...., N-1 .

21
Substituting for f.

N-1 -j/2TAmn

X(mf) = z x(nT )e \n /

n=0

and, using the twiddle factor ]/i^,

N-1 mn

X(mf) = z x(nT-)W^ . n=0 '^

Thus, there are nominally N multiplications of the data samples x('^"'^s)

by the twiddle factor Vi^, and N complex additions involved in the DFT.

The X(mf) are the amplitude coefficients of the transform, where

m = corresponds to the dc component,

m = 1 corresponds to the fundamental component.

m = N-1 corresponds to the Nth harmonic component.

These coefficients are, in general, complex by virtue of the complex

twiddle factors. Of particular interest, we note that

Wk = [W(N-k)]*

where * denotes complex conjugate.

The proof for this equality is as follows:

-j /M (N-k)

=

j e m

(N-k)

+ ,J27T - j/2TTk

= e e

= e W)

_ w^

22
Hence

.N-

,(N/2)-l = [-w(N/2 + 1)]*

For the DFT then.

X(f) = X*[(N-l)f]

X(2f) = X*[(N-2)f]

X[(N/2 - l)f] = X [N/2 + l)f]

provided that N is even. The real frequency components of the DFT

are thus symmetrical about N/2, while the imaginary components are reflected about the horizontal axis as shown in figure 9 below.

Re[X(mf)]

r I

H—I—I—XJ«-H 1

1—I1 2 • • • N/2 ... N-1

-I—^ m

Im[X(mf)]

I 1,—I,—,

I—TH-i—I—

r^ -^ m

Figure 9. Real and imaginary components of the DFT.

23
The "negative" frequency terms of the continuous Fourier transform

are analogous to the DFT coefficients beyond N/2, but less than or

equal to N-1 . This property is due to the period extension of the X(mf)

spectrum since

X(0) = X(Nf)

X(f) = X[(N+l)f]

X(2f) = X[(N+2)f]

X[(N/2 - l)f] = X[(N + N/2 - l)f] .

Thus it is that with a 64-point FFT (N = 64), we can obtain the N/2 = 32

coefficients or amplitudes for the dc (m = 0), fundamental (m = 1),

and 30 harmonics (m = 2, 3, ...,31) of the input signal. Also,

because of the complex conjugate nature of the 32 twiddle factors,

the latter 16 values of Wk are the same as the first 16 with only the

sign of the imaginary part changed. A 16 entry look-up table is

included in the distortion program with a simple decoding scheme to

determine the real and imaginary parts and to set the signs correctly.

The total calculation time for the 64-point FFT with 16-bit resolution

is typically 400 ms when executed on the IMP-16C.

3. CIRCUIT DESCRIPTION

The basic architecture of this instrument is described in section 2.1

The purpose of this section is to provide a more detailed description

of the functional blocks comprising the low-frequency sampling

voltmeter as shown in figure 1. In the discussion of these circuits,

reference is often made to the various schematic drawings given in

appendix C. Photographs, corresponding to each printed circuit board,

are given in appendix D. As can be seen in photo 8, which is a back

view of the voltmeter with the back panel removed, a card cage is used

to contain the IMP-16C microcomputer board, the memory, timing, and

control I/O board, and the data acquisition module or A/D board (from

top to bottom, respectively). Photo 7 is a front view with the front

panel dropped down to show the backplane of the card cage. The

display board and the shielded enclosure containing the preamplifier

(which are both mounted on the front panel) also can be seen in this

photo. Table 1, on the following two pages, provides a back panel

wiring diagram which identifies the signal name and how it relates

to the pins on the connectors (Jl , J3, and J5) used for the CPU,

I/O, and A/D boards.

24
Table 1

Backpl ane wiring diagram

Name Jl (CPU) J3 (I/O) J5 (A/D)

ADO 10 66

INTRA 15 56

AD7 18 80

AD6 20 78

AD2 23 68

ADl 24 60

AD3 25 91

BD8 27 24

ADS 28 74

AD4 29 76

MDO 40 128

MDl 41 130

MD2 43 132

MD3 44 126

MD4 47 124 128

MD5 48 122 126

MD6 50 120 124

MD7 52 118 122

BD5 56 30

BDl 58 42

BD4 59 28

BD3 61 38

MDl 4 62 104 108

BD7 63 26

BD2 64 40

BD6 65 32

B09 67 22

BDll 68 18

BDl 4 69 12

BDl 5 70 10

BDIO 73 16

BDl 3 74 14

BDl 2 75 20

MDIO 76 116 120

MDl 3 77 106 110

25
GND

Table 1 (cont.)

Name J1 (CPU ) J3 (I/O) J5 (A/D)

44

108 112

112 116

114 118

110 114

96

102 106

90

86

82

94

54

48

136

92

100

GND

GND

GND

GND

GND

GND

84

133 133

131 131

135 135

88 88

129 82

136 70

74 GND

76 GND

78 GND

80 GND

68 GND

1117

13. 15

52

BDO 60

MD12 78

MD8 82

MD9 87

MDll 88

AD13 101

MD15 108

ADll 109

ADIO 110

AD9 112

AD14 115

WRMP 120

CLK 128

JC12 129

RAM SELECT 21

AD15 116

AD12 114

CD15 36

JC14 104

JC15 107

INTCTL, INTEN 85, 131

CPINT 118

JC13 119

JC12 129

AD8 111

RLYA

RLYB

RLYC

25T

27T

158, 14T, 17T

A/D MVX ADR

II II II

II II II

II II II

II II II +15 VDC

-15 VDC

Analog GND

+12 VDC

-12 VDC 31

26
3.1 Microcomputer Board

The IMP-16C is a 16-bit parallel processor configured around

National Semiconductor GPC/P (General Purpose Controller/Processor)

MOS/LSI devices. These MOS/LSI devices are two read-only-memories

(ROM) and four register/arithmetic logic units. Since each logic

unit handles four bits, 16-bit processing is handled by connecting

four units in parallel. Memory on the IMP-16C microcomputer card

consists of 256 words of RAM. Data (BD-bus) from/to the peripheral

devices and add-on memory (MD-bus) are routed through an input

multiplexer on the IMP-16C card to the central processing unit (CPU).

Data from/to the on-card memory is also processed in this way.

Address data is available via the 16-bit AD-bus.

All the peripheral devices to the IMP-16C microcomputer (sampling

rate generator, A/D converter, display, etc.) are memory mapped.

The following discussion briefly describes each peripheral and its

function, and indicates its associated memory addresses. A linear

address scheme is used to address these peripheral devices. Address

data from the microcomputer's AD-bus is decoded on the NBS 722 7909A

board (IC 31, 32, 33, and 34), and the decoded signals are routed from

there to the rest of the system (see schematic 4). Data from the

IMP-16C are latched into IC 13, 14, and 15 of NBS 722 7909A for the

peripheral devices via the BD-bus. Latching occurs coincident with

the write memory pulse (WRMP) which is generated during all write to

memory cycles of the IMP-16C microcomputer.

3.2 Sampling Rate Generator (Schematic 4, NBS 722 7909A)

Address 8800 Hex - Clock data for the sampling rate generator is

latched from the BD bus, coincident with hex address 8800 and the

WRMP pulse. The sampling rate generator, functioning as a programmable

interval timer, uses the data word to control the period of the

conversion pulses output to the A/D converter.

Clock data appears on the BD bus in the following format:

Bit position 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

Data PS PS PS M M M MMMMMMMMMM

where PS = frequency prescaler bits

M = mantissa .

27
The 16-bit data word consists of two parts as shown: a 3-bit

frequency prescaler and a 13-bit mantissa. The prescaler part

is also latched into the frequency prescaler circuitry (IC 9, 10, 11,

12), which divides the clock input (5.76 MHz CPU clock) by 1 , 4, 16,

64, 256, 1024, and 4069.

One of the output frequencies selected by the 3-bit prescaler

code is sent to a down counter (IC 5, 6, 7, 8) preset by the 13-bit

mantissa. Once initialized in this way, the down counter is preset

after each zero count to the 13-bit mantissa value. The 13-bit

mantissa is stored in latches (IC 1, 2, 3, 4) from the BD latches

during the first 8800 hex address. At each zero count of the down

counter, a 10 ys pulse is generated (IC 18) and sent to the A/D

converter as a convert command (pin 129, J3).

3.3 A/D Converter (Schematic 5, NBS 722 79141A)

The A/D converter chosen for this application has 12-bit resolution

(11-bits + sign) with a conversion time of 12 ys. The A/D converter

is part of the data acquisition module (Datel MDAS-8D) which contains

an analog multiplexer, an instrumentation amplifier, and a S/H

amplifier. The instrumentation amplifier is designed with internal

feedback resistors to allow three fixed gains (4, 2, 1), providing a full-scale output from the A/D converter for inputs of ±2.5 V,

±5 V, and ±10 V. These ranges are selected via the microcomputer

by the switching of relays A, B, and C.

Address 8040 Hex - The control word to set the range for the A/D

converter is latched into IC 21 of the NBS 722 7909A board from the

BD latches on this board during hex address 8040 and the WRMP pulse.

Outputs from IC 21 are used to drive the coils of the range setting

relays (A, B, C) on the A/D board.

The following format is used on the BD bus:

Bit position 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

Data x x x x x x xxDDDDxxxx

where x = don't care

DDDD = 0000 = 10 V range

DDDD = 0010 = 5 V range

DDDD =0011 = 2.5 V range

28
The data acquisition module has an analog multiplexer on its

front end with eight differential input channels. The input channel

can be selected by performing the following action:

Address 8200 Hex - The 3-bit multiplexer address code is latched

into the data acquisition module, coincident with this address and

the WRMP pulse. The only multiplexer channel address presently used

in the voltmeter is a code of all zeros. This code is hardwired at

the data acquisition module multiplexer address points.

For outputs from the A/D converter, the following action applies:

Address 8400 Hex - Coincident with this address, the tristate outputs

of the data acquisition module are enabled and converter data is

placed on the MD bus (MOO 4-15).

3.4 Program Memory (Schematic 4, NBS 722 7909A)

The entire program code for controlling the operations of the

Low-Frequency (LF) Sampling Voltmeter is contained in EPROM (IC 29, 30)

The EPROMs are Intel type 2716s configured as a 2K by 16-bit memory.

Address 3000 - 3800 Hex - The 2716 EPROM select lines are enabled

with these addresses. For startup, these addresses are also mapped to

F800-FFFF.

3.5 Preamplifier (Schematic 2, NBS 722 79284A)

The preamplifier hardware contains a modular instrumentation

amplifier (Analog Devices 606J) which is gain-controlled by relayselectable resistors. The AD606J amplifier was chosen mainly for

its low noise specification. Decade range selection for the voltmeter

is accomplished with different preamplifier and data acquisition

module gain settings. The preamplifier scales input signals in the

range from 10 mv to 10 V rms (full scale) to a level of 7 V rms. For this purpose, four-decade gain steps are provided (by means of

the resistors, trimmable potentiometers, and relays) with gains of

700, 70, 7, and 0.7. The input signal may be either single-ended or differential with a common mode voltage of less than 1 V.

To correct for changes in offset of the AD606J amplifier with

different gain settings, an auxiliary null adjustment circuit is

required. An operational amplifier (Teledyne TP 1319) is used to

supply a small positive or negative voltage to correct for the

variable bias-current induced offsets when the gain-setting resistors

are changed.

Address 8020 Hex - The gain control code for the preamplifier

is latched into IC 15 of the NBS 722 79026A display board, coincident

with the WRMP pulse and this address. The output of the latch is

then buffered to drive the coils of the gain controlling relays.

29
The following format is used on the BD bus:

Bit position 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

Data X X x x x x xxxxxxDDDD

where x = don't care

DDDD = 0111 = relay A, B, C activated - 10 V range

DDDD = 0100 = relay C activated - 100 mV range

DDDD = 1000 = relay D activated - 10 mV range

DDDD = 0000 = no relays activated - 1 V range .

3.6 Front Panel Numerical Display/LEDs (Schematic 3, NBS 722 79026A)

Address 8080 Hex - Numerical display data is latched into IC 2,

3, 4, 5, and 6, coincident with the WRMP pulse and this address.

Selection of the appropriate latch occurs simultaneously, with IC 8

used as a digit decoder. Decimal point data reside in the IC 6 latch

while first, second, third, and fourth digit numerical data reside in

IC 2, 3, 4, and 5, respectively.

The following format is used on the BD bus:

Bit position 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

Data X X x x x x xxDDDDIIII

where x = don't care nil = numerical data code (0-9 BCD)

DDDD = digit to be selected (1-6 BCD) .

Coincident with all IC 6 updates is a momentary pulsing of LED 13

(display update indicator) through IC 14.

Address 8010 Hex - LED display data is latched into IC 10 and 11 of the display board, coincident with the WRMP pulse and this address.

The latch outputs are buffered by IC 12 and 13 which drive the LEDs.

The following format is used on the BD bus:

Bit position 1 5 14 13 1 2 11 10 9 8 7 6 5 4 3 2 10

Data X X x x 12* 11* 10* 9* 8* 7* 6* 5* 4* 3* 2* 1*

30
where x = don't care

* - each numerical digit represents an LED position on the display

board (see schematic 3). If a logic one or zero exists in

any of these positions, there is LED activation or no LED

activation, respectively.

3.7 Front Panel Switches (Schematic 6)

Address 8100 Hex - Data representing the front panel switch

positions is read from latches IC 26 and 27 of the NBS 722 7909A

board, coincident with this address. The switches are connected to

these latches via the external 50 line connector and cable from the

CPU board to the display board. Switch data is strobed into the

latches automatically (by IC 20 on the NBS 722 7909A board) when

these latches are addressed by the CPU.

4. OPERATING INSTRUCTIONS

4.1 Installation

The NBS Low-Frequency Sampling Voltmeter mounts onto a standard

19-inch equipment rack. Ensure adequate ventilation. The voltmeter

is powered from a nominal 117 V, 60 Hz ac line.

4.2 Controls

4.2.1 Power Switch

The power switch is the toggle switch located on the front panel

(see photo 1 ).

4.2.2 RMS AC + DC, RMS AC, Freq., Dist.

These functions are performed and displayed individually by the

voltmeter by pushing the appropriate front panel button (see photo 1).

If the signal has already been obtained (that is, a number is displayed

on the front panel LED numerical display) and the user desires to see another function, the voltmeter will blank out the display momentarily

to perform the new operation once the appropriate pushbutton has been

depressed. If either the frequency or amplitude of the incoming

signal varies significantly, the display will blank out and take two

signal periods before new data is displayed (see section 2, Theory of

Operation). The voltmeter averages the last computed rms value with

the previous 16 values of the incoming signal stored in RAM on the IMP-16C microcomputer board. If the latest value differs by more

than ±1 percent from the running average, this value is then displayed

and a new cycle of averaging readings is begun. Consequently, the

operator must wait for the voltmeter readings to stabilize if the

rms value is changing, particularly at frequencies below 1 Hz. Also,

the operator is cautioned to be aware that this averaging feature

does not permit simple multiplexing of the input of the voltmeter to

several sources.

31
4.2.3 10 mV, 100 mV, 1 V, 10 V Pushbuttons

The operator selects the range manually by pushing the appropriate

button. This action will activate an entire measurement sequence for

the voltmeter (see section 2, Theory of Operation) with the internal

preamplifier set to the appropriate range value. If the instrument

cannot make a measurement on that selected range, it will automatically

sequence to the correct range (see section 4.2.4, Autoranging). When

the incoming signal level (as indicated by the numerical display) is

within the full-scale value of the next lowest range (see section

4.3.6), a more accurate reading can be obtained by manually selecting

this lower range.

4.2.4 Autoranging

This feature exists as an internal software control for the

instrument to automatically select the appropriate range for measurement

purposes and will override an inappropriate range setting the user inadvertently selects. However, this operation takes time, extending

the initial measurement sequence, as the instrument must range up over each of the possible ranges from an initial range setting.

4.2.5 Reset

Pushing this button causes an entire measurement cycle to be

initiated regardless of anything else.

4.3 Indicators

All controls are indicated active by the voltmeter when the LED

corresponding to a given control is turned ON.

4.3.1 Reset

The LED indicator for this function is always ON when the period

of the incoming signal has not been determined and sampling has not

been successful (see section 2, Theory of Operation). Otherwise,

this LED is OFF indicating that the period of the incoming signal is

known and samples have been taken.

4.3.2 Display

This LED is momentarily ON during each update to the display. If

the Reset LED is OFF, the Display LED will be activated at a fixed

rate depending upon the frequency of the incoming signal.

4.3.3 Overload

This LED indicates that too large a signal (>10 V rms) or too

large an offset (>10 V) is present at the input terminals.

32
4.3.4 RMS AC + DC, RMS AC, Freq., Dist.

The instrument will indicate which function is being performed by

activating the appropriate LED above the function pushbutton.

4.3.5 Front Panel Numerical Display

This display is a five digit LED numerical display. If the function

is frequency, the display will be in hertz. If the function is Dist.

(Distortion), the display is in percent.

If the function is rms ac + dc or rms ac, the function is in volts.

Volts or millivolts are indicated by the two LEDS located near the

front panel LED numerical display.

4.3.6 10 mV, 100 mV, 1 V, 10 V Ranges

The instrument indicates on what range it is currently operating

by activating the appropriate LED.

4.4 Signal Input

The incoming signal is applied to the instrument via the front

panel banana plugs. These plugs route to a differential amplifier

with HIGH indicating the high side of the differential amplifier and

LOW indicating the low side. GND indicates instrument ground.

The maximum signal between HIGH and LOW terminals is 10 V rms for

a measurement to be obtained. The maximum offset between the LOW and

GND terminals is 10 V for a measurement to be obtained.

5. ERROR ANALYSIS

The performance of the Low-Frequency Sampling Voltmeter described

herein is dependent upon both the software implementation of the

measurement algorithms described in section 2.2 and the hardware

implementation described in section 3. The algorithms assume ideal

sampling of the input signal and the conversion to digital values.

A brief discussion is given here of the measurement errors due to

offset and gain in the preamplifier and data acquisition channel,

quantization amd nonlinearity of the A/D converter, and timing jitter

in the S/H amplifier and sampling rate clock. A more complete analysis

of these errors is provided in [11].

5.1 RMS Zero and Gain Error

The preamplifier circuit and data acquisition module (instrumentation

amplifier, S/H, and A/D converter) are described in sections 3.3 and

3.5. In this analysis, it is assumed that the transfer function of

the data acquisition module is essentially linear for the 2.5, 5,

33
and 10 V ranges provided. Hence, the accuracy of this data acquisition

hardware is dependent on how well two points on the transfer function

(generally zero and full scale) can be adjusted with the trimpots

provided on the module.

The accuracy of the data acquisition module was tested by measuring

dc voltages produced by a stable source. The output from the source

was also measured by a digital voltmeter, calibrated to an accuracy

of better than 50 ppm. Before adjusting the offset (zero) and gain

controls, 100 readings were taken from the A/D converter at each of

several voltages on the three different ranges and compared to

corresponding readings of the DVM. This data is summarized in the

plots given in figure 10. After the data were taken, the gain and

offset errors were then adjusted to near zero for the three ranges.

The resultant gain and offset errors, compiled from averaging 400

readings at each point, are listed in table 2 below. As can be seen,

considerable improvement can be made in the unadjusted error by

trimming the offset and gain controls, although with only one set of

adjustments, all the zero and gain errors cannot be simultaneously

adjusted to zero.

Table 2

Final gain and offset errors after adjustment

of the A/D converter

5 V range

Input

voltage

(volts)

-4.9963

+4.9988

Error

(% of fs)

-0.00098

-0.00220

Gain error

(% of fs/fs)

Offset

error

:% of fs)

0.00122 -0.00159

2.5 V range -2.4994

+2.4984

0.00293

•0.06641

-0.06347 +0.00347

10 V range -9.99760

+9.97803

+0.06592

+0.05786

-0.00806 +0.06189

34
a;c

fO

So

>

O)

OJ en

cri c

c to ro iS-

+-> +J r—

1

o

o >

>

un

c^o

o

+

C\J +

OJU

4-O

Q.

i- • O c/) M- J- O) O

jO J-

<u

4-> !-> t- Qi

0) (/) >^-

C4- O O

O

-D O C

^^ fO <: c

aj -r4-> en

14_ <u

1-

s_ o

SOJ 4-> c

73 O)

O) E

J- (-> 3 CO

to Z3

fo •>—

>

cu -a

CVJ

t

a>

oLD

I

LDO

+

o

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o

+

oo

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+

(aLBDS Lin^ io %) yoy^H

35
Appendix A provides a calibration procedure (section A.l .2) for

adjusting the "BAL" and "NULL" trimpots of the preamplifier to

compensate for its offset on all four ranges of the voltmeter.

Following this procedure will provide preamplifier offset errors of

0.1 percent of full scale or less.

The residual error at the ± full-scale limits of any of the

four voltmeter ranges can thus be translated into an offset (zero) error eg and gain error eg for the instrument. These errors,

in combination with the magnitudes of the ac (Mac) ^nd dc (M^c)

components of the signal, produce the following expression for the

rms (zero and gain) measurement error:

rms error = V

[(1 - ^g)"dc * =0^" * t(l - ^g)"ac]

r

-1

V C^dc'' ^ ("ac''

where

Sq = gain error in percent of full scale/full scale

eq = offset error in percent of full scale

McIq = dc component of signal

Mqc = 3C component of signal .

Generally, M^c is some fraction of M^^ as is the offset eq,

where M^c is kept near full scale. This expression can thus be

evaluated using the gain and offset errors for the data acquisition

module and the preamplifier discussed above.

For a signal with Mj^ = 0.1 M^q (the maximum allowed by the signal

model) and M^c = full scale so that gq = offset error in percent

of full scale (kMgc), the rms error expression is then

36
rms error = V[(1 - yo.l M,, ^kM^/^[(1 -^g)\f .1

^ [(1 -,)o.i.k]2M^^Mi -V'4

V

^-^^ ^ac

^[(1 - £g)0.1 + k]^ + (1 - e^f _^

where J 1.01

k = eq = offset error in percent of full scale

= gq (preamplifier) + eq (data acquisition module) .

Using the 10 V range gain and offset errors from table 2 (-0.008 percent

and 0.062 percent, respectively) and eq (preamplifier) = 0.1 percent,

the rms error can be calculated to equal 0.024 percent. Using the

2.5 V range gain and offset errors (-0.063 percent and 0.00347 percent,

respectively) and eq (preamplifier) = 0.1 percent, the rms error

can be calculated to equal 0.073 percent. Ideally, if the gain error can be assumed to be negligible (see appendix A, section A. 1.3),

then a further simplification gives

V

(0.1 + e.f + 1 rms error = -1 > for Sg " ^ • ^u01

The same total maximum offset error of 0.162 percent of full scale

(10 V range) will then cause an rms error of only 0.016 percent.

5.2 Quantization Error

The measurement error of the voltmeter is also due in part to

the error attributed to finite quantization of the input signal by

the A/D converter. Under certain conditions, this error can be

approximated by random noise with zero mean and variance (standard

deviation squared) of q2/12, where q is the smallest quantization

interval, or one least significant bit (LSB) of the A/D converter [13],

The assumption for this result to be true is that when the signal

is located within a particular quantization interval, the difference

(or error) between the continuous-time signal and the particular

quantization level is uniformly distributed over the quantization

interval (i.e., a uniform error probability distribution).

37
The rms value of the input signal E(t) has been described

earlier (section 2.2.3) to be given by

=rms ^,= i/t ^ [E(tk)]^

where there are exactly N samples within one period T (nominally

128 in this case). Or, letting the values of E(t) at time values

t|< be denoted by E^,

-rms " %/t M^ (^k)

With added random noise, R^, the rms value of the signal plus noise

is then

Erms = Ha/I z (Ek + Rk)^

which, for small Rk, is approximately

'^^^v^i < ^?y

It can then be shown that the variance (a^) of E^^^^ due to the

random noise is I^li ^here q' = 2q, or a^ = ^• An initial

criterion for determining the A/D converter resolution was that

the (random) quantization noise contributes no more than 0.05 percent

error (3a limit) to the noise-free rms value for a reasonable

number of samples. Hence, if we assume 100 samples per period, then

3a = 0.0005 /N

38
or.

2 . a

= 0.0005 /N

2 . 2

= 4q_

12

Thus, q = 0.002887 which requires a converter with 9 bits (plus a sign bit for bipolar operation).

To verify these calculations, however, a series of computer

simulation tests were performed. For these tests, 20 sine waves

with rms values of unity and with random phase shifts (Start Angle) were generated, quantized to a specific number of bits (8, 9, and

12). The BASIC program and printouts for several sets of simulation

calculations are contained in [11]. For each set of 20 calculations

(20 different starting angles to randomize the quantization error),

the rms value was calculated, based on 10 and 100 samples. The

results of these calculations are tabulated below:

Converter resolution

(including sign bit)

12 bits

9 bits

8 bits

8 bits

RMS error

0.0000950

0.0006533!

0.0013

0.0005013[

la limit for 10 samples

la limit for 100 samples

These values agree rather well with the ^t^ Al prediction.

The wide range of input signals (2 mV to 10 V) requires the

preamplifier described before, having adjustable gains of 1, 10,

and 100 to normalize the signal before it is applied to the data

acquisition module. Even so, not all signals will span the range

of the instrumentation amplifier, S/H circuit, and A/D converter of

the data acquisition module; however, at least 10 bits of resolution

are needed for the smallest signal, as discussed above. A 12-bit

converter was chosen, therefore, because of the required resolution

and accuracy. The gain setting of the instrumentation amplifier

in the data acquisition module must then be no larger than four

times the next lower setting, so that the signal will always use 2^2 -JQ full scale/4 = —5- =2 or 10 bits of the converter. In

39
practice, this scaling is accomplished by having gains of 1 , 2, and

4 in the instrumentation amplifier (data acquisition module). With

a maximum change of 2.5 between ranges, the maximum random rms measurement error due to finite quantization is then

random rms error < — = Vi

©"'

V

1 I

l J = 0.033 percent

5.3 A/D Converter Nonlinearity Errors

The A/D converter in the data acquisition module is of the

successive approximation type. This type of converter exhibits

both linearity and differential linearity errors. Linearity errors

indicate that the digital output produced by the converter is not

exactly a linear function of the input voltage, whereas differential

linearity errors are a measure of the variation in input signal

change associated with a one-bit change in the digital output.

These errors vary, depending on the particular location along the

converter's transfer characteristic.

Figures 11 and 12 show plots from linearity tests made on two

different data acquisition modules of the type used in the LowFrequency Sampling Voltmeter. With the input multiplexer set for

one channel and the S/H amplifier operating in the nominal track and

hold mode, 1024 evenly spaced output codes of the 10 most significant

bits of the A/D converter were tested by measuring their associated

transition edge voltages [17]. As described in [17], the transition

edge voltages (where adjacent output codes are obtained on a 50

percent basis) accurately define the transfer characteristic.

The center plot is of the measured error data of the data

acquisition module, obtained by comparing the transition edge

voltages of the module with the output voltages from a 20-bit

reference D/A converter (used in the test set), at corresponding

digital codes. In the case of figure 11, the maximum linearity

errors of approximately ±1 LSB occur at position 777, or

' 777-512) X lOV = 5.2 V, and at position 241, or "5T2 J 512-241) X (-10 V) = -5.3 V. In figure 12 the linearity of this

.~5T2 J

particular module is seen to be somewhat better. The rms value of the error data is 0.275 LSB as compared to 0.392 LSB for the module of

figure 11

.

40
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Significant discontinuities in these plots are seen to occur

at half scale and at one-quarter and three-quarters scale, which are major code transition points. Assuming that the linearity error

data would not change significantly had all 12 bits of the converter

been exercised, an estimate of the worst case differential linearity

error can be made from the amplitude of these discontinuities.

From the plots for both modules tested, it can be seen that the

maximum differential linearity error for these units can be estimated

to be 1 LSB.

A good approximation of the measurement error contributed by

the nonlinearity of the data acquisition module (primarily, the A/D

converter) can be made from the test data in figures 11 and 12. In

particular, the worst case error due to either linearity or differential linearity is ~1 LSB or,

nonlinearity error (max) = l/(2l2) x 100 percent of full scale

= 0.0244 percent .

For an explanation of the top and bottom plots shown in figures

11 and 12, the reader is referred to [17]. Briefly, these plots

are the results of further analysis of the linearity error data.

A Walsh transform is made on this error data which is taken to

represent a uniformly sampled function having a period of 2N

samples where N, in this case, is 10. Walsh series functions are a set of orthogonal functions analogous to a Fourier series, differing

primarily in that Walsh functions are square-like rather than

sinusoidal. A reconstruction (inverse transform) of the error data

can then be made (top plot) which is a minimum mean squared error representation of the actual measured error data (center plot).

Finally, the difference between these two data sets is used to

plot a residue function (bottom plot). This function is representative

of the effective coupling between bits, or superposition errors.

In general, these errors establish a practical limit beyond which

no simple adjustments or corrections to the converter are useful.

5.4 Timing Errors

Besides the types of direct amplitude errors described in

sections 5.1, 5.2, and 5.3 above, the timing (sampling) jitter in

the S/H amplifier and in the sampling rate clock can be translated

into their equivalent amplitude errors. Errors associated with the

S/H amplifier that can contribute errors when measuring the rms value of a signal are aperture time jitter, acquisition time, and

droop rate [14,15]. This same type of sampling time uncertainty

also applies to the frequency instability of the sample rate clock.

For this sampling voltmeter application, the aperture time

itself is unimportant so long as it remains constant. The aperture

time jitter, however, will appear as a random noise voltage

43
superimposed on the input signal samples. The maximum magnitude

of this noise can be estimated from the aperture time jitter and

the maximum first derivative of the input signal [16]. Letting

E(t) = A sin u)t, then

E' (t) = wA cos wt

or,

E' (t)max = ^A = amp! itude jitter

'"°^ aperture time jitter

Representing amplitude jitter as kA, then

« kA ^^ aperture time jitter

or,

k = w (aperture time jitter) .

Since the S/H amplifier used in the voltmeter has an aperture time

jitter of 50 ns less,

•^(max) 1 ^"^ (^2^ Hz)(50 x 10-9)

< 0.000377 .

Hence, the maximum noise jitter is less than 0.038 percent of the

peak input amplitude which corresponds to an rms noise error of

0.027 percent.

Acquisition time error occurs when the S/H amplifier is not

given sufficient time during the sample mode to allow the output

delay and settling time to occur when acquiring the input signal

again. The droop rate error of the S/H amplifier is a function of

acquisition time, as well as of present input magnitude, previously

held input magnitude, and length of required hold time. The output

signal of the S/H amplifier must be held within ±1/2 LSB for

the duration of the A/D conversion process in order to introduce

zero (or negligible) error. For the 12-bit A/D converter used in

the data acquisition module, this requirement translates into

maintaining the held value to an accuracy of ±0.01 percent for

approximately 12 ys.

The frequency instability of the sample rate clock contributes

an amplitude error in the same way as aperture time jitter, discussed

above. That is, the conversion signal from the sample rate clock

may have a random jitter superimposed on an otherwise uniform timing

interval that manifests itself as a random noise voltage on the

44
input signal samples. The maximum magnitude of the rms voltage

noise can be estimated from the rms value of the clock jitter and

the maximum value of the first derivative of the input signal [13],

That is,

rms error (clock jitter) _< a (max first derivative)

where a = rms value of the clock jitter

or, rms error (clock jitter) _< a (wA) which is equal to aw

as a percent of the input signal amplitude A. Because the sampling

clock rate is a fixed multiple of the input signal frequency (128x),

the rms error due to clock jitter is constant. For a 10 Hz signal

the rms value of the clock jitter (a) was measured as 140 ns,

which translates to

rms error (clock jitter) _< 140 x 10-9(2Tr 10)

_< 0.00088 percent .

Because of the integrated construction of the data acquisition

module used, it is not possible to directly evaluate the dynamic

characteristics of the internal S/H amplifier. However, a test

was performed on the instrumentation amplifier, S/H amplifier,

and A/D converter combination by applying a low distortion sine wave source (<0.02 percent THD) to the module, and least squares

fitting the digital output data to a pure sinusoid. After

correcting for zero and gain errors, the standard deviation

for the fit was 0.02 percent. Since this value is comparable to

the distortion in the source itself, the previous error estimates

appear to be reasonable.

6. INSTRUMENT PERFORMANCE

The resulting performance obtained with the initial LF Sampling

Voltmeter prototype and the seven subsequent models (one NBS unit

and six for use in the DoD Metrology Centers) will be described in

this section. These evaluation tests show typical performance data

and do not represent the results of a set of statistically based

performance tests.

6.1 Frequency (or. Period) Tests

A commercially available frequency counter with an accuracy of

better than 0.01 percent (Tektronix Model DC505) was used to check

the accuracy of the frequency (or, period) measuring function. The

data shown in table 3 below are from readings taken with the initial

LF Sampling Voltmeter prototype [11]:

45
Table 3

Calibration data for the frequency function of the LF Sampling Voltmeter

using an 0.01 percent accurate Tektronix 505A frequency

counter (in the period measuring mode)

505A frequency

(Hz)

LF Sampling Voltmeter

(Hz)

Error

(% of reading)

0.10121 0.101 -0.2ia

1.0123 1.012 -0.03

10.125 10.12 -0.05

14.030 14.03 0.00

30.000 30.01 . +0.03

44.503 44.50 -0.01

48.026 48.07 +0.09

55.026 55.09 +0.12

56.363 56.40 +0.07

57.741 57.81 +0.12

60.68 60.70 +0.03

68.743 68.76 +0.03

78.380 78.42 +0.05

102.04 102.1 +0.06

119.00 119.0 0.00

aResolution of 1 percent limited the accuracy of the reading,

46
These data seem to indicate that the target accuracy of

±0.1 percent of reading is achievable for most frequencies.

Limited display resolution prevents a good comparison at the

0.101 Hz value. The random error is most likely due to slight

variations in the period as determined by the exact period error

function described in section 2.2.2. The small systematic error is

probably due to the design of the sample rate clock. A finite time is

required to preset the counters in the sample rate clock circuit,

after each output pulse, and this reset time adds a larger percentage

error at higher frequencies. This effect was born out in tests

made on the subsequent units, as shown in table 4 below:

Table 4

Frequency test on engineering model

505A frequency

(Hz)

LF Sampling Voltmeter

(Hz)

Error

(% of reading)

0.0999 0.099a -0.9a

1.0984 1.098 -0.04

3.594 3.594 0.00

11.017 11.02 +0.03

20.013 20.02 +0.03

30.050 30.070 +0.067

40.034 40.08 +0.11

68.070 68.18 +0.16

119.19 119.4 +0.18

aResolution of 1 percent limited the accuracy of the reading.

Here we can see the greater effect of the reset time such that

at higher frequencies (>40 Hz) the frequency displayed by the LF

Sampling Voltmeter is slightly higher than the actual frequency.

47
6.2 RMS Voltage Tests

As part of the final evaluation of the initial LF Sampling

Voltmeter prototype, this instrument was tested in comparison with

a commercial 5-1/2 digit ac average responding digital voltmeter

(Data Precision 2540A1 ) . These tests were conducted using a high

stability sine wave generator specially constructed for this purpose

[11]. The requirements for the generator were good cycle-to-cycle

amplitude and frequency stability, a frequency range of 0.1 Hz to

120 Hz, and an output adjustable in steps from zero to 7 V rms. Therefore, a digitally synthesized waveform was generated by sending

a series of digital values from a read-only-memory (ROM) containing

the digital values of a sine wave to a digital-to-analog converter

(DAC). Another reason for using this method was the ability to

generate a sine wave with a predetermined distortion so that the

distortion measurement algorithm of the LF Sampling Voltmeter could

also be checked. The generator design, detailed in [11], provided a sinusoidal source whose average ac voltage at 20 Hz was measured to

be only 0.01 percent different than at 100 Hz. An active two-pole

low-pass Butterworth filter (flat to within 0.1 percent from dc to

105 Hz) was utilized in the output design of the generator. This

circuit effectively filters out "glitch" transients in the output of

the 12-bit DAC (used to produce the stepped analog sine wave) and to

smooth this output into the final sinusoidal form. Then, the

calibrated sine wave generator was used to verify the performance of

the 2540A1 at 20 Hz. Table 5, on the next page, shows the measurement

data for comparison between the 2540A1 digital voltmeter and the

prototype sampling voltmeter.

48
Table 5

Calibration of the rms ac + dc function of the voltmeter by the

Data Precision 2540A1 voltmeter at 20 Hz using the waveform generator.

Amplitude

setting

2540A1

(volts)

11 7.0700

10 6.4281

9 5.7865

8 5.1425

7 4.5002

6 3.8569

5 3.2133

4 2.5713

3 1.9283

2 1.2860

1 0.6430

LF Sampling

Voltmeter

(volts)

D(%

ifferencea

of reading)

overrange -

6.425 -0.01

5.783 -0.03

5.142 +0.02

4.498 -0.01

3.854 -0.04

3.212 -0.01

2.571 +0.02

1.928 +0.02

1.285 -0.04

0.643 +0.03

aThe calculated output of the waveform generator at 20 Hz is

7.0676 V for setting 11. A correction of -0.034 percent (calculated

minus measured difference for 2540A1 at setting 11) is applied to all

the 2540A1 readings before the differences between the two instruments

are calculated.

49
As a further test of the ac rms measurement accuracy of the

initial prototype, it was tested with the multi-junction thermal

converter-based NBS AC Voltmeter/Calibrator developed at NBS [4,5].

This instrument contains a built-in, ROM-based ac voltage calibrator

with ±0.02 percent of reading accuracy from 2 mV to 7 V rms for

the 0.1 to 50 Hz frequency range. Table 6 shows test data on the LF

Sampling Voltmeter prototype using the NBS AC Voltage Calibrator [11].

Table 6

AC rms tests of prototype LF Sampling Voltmeter

Frequency

(Hz)

NBS AC

Voltage Calibrator

(volts)

LF Sampling

Voltmeter

(volts)

6.386

(%

Error

of reading)

50 6.384 +0.03

5.070 5.070 0.00

3.159 3.160 +0.03

10 3.159 3.161 +0.06

5.072 5.074 +0.04

The data in tables 5 and 6 above indicate that the performance of

the initial LF Sampling Voltmeter met the rms voltage measurement

accuracy goal of ±0.1 percent of reading. However, an important

additional performance verification test was subsequently made on the engineering prototype which contains the (four-decade gain setting)

preamplifier. The description of this preamplifier is given in

section 3.5. These seven engineering models have four input ranges

of 10 mV, 100 mV, 1 V, and 10 V (full scale). Table 7, on the next

page, shows test data on the engineering prototype of the LF Sampling

Voltmeter with readings taken by the NBS AC Voltmeter/Calibrator.

50
Table 7

Tests of the LF Sampling Voltmeter (with preamplifier),

using the NBS AC Voltage Calibrator Standard

50 Hz

10 Hz

1 Hz

0.1 Hz

50 Hz

10 Hz

1 Hz

0.1 Hz

NBS AC Voltage Calibrator

(volts)

LF Sampling

Voltmeter

(volts)

6.383

3.159

2.243

Error

% of reading

6.384

3.159

2.242

-0.015

-0.00

+0.04

6.384

3.159

2.242

6.382

3.157

2.242

-0.03

-0.06

0.00

6.384

3.159

2.242

6.382

3.158

2.243

-0.03

-0.03

-0.04

6.384

3.158

2.242

6.384

3.158

2.242

0.00

0.00

0.00

0.6384

0.3159

0.2242

0.6381

0.3158

0.2242

-0.05

-0.03

0.00

0.6384

0.3159

0.2242

0.6384

0.3158

0.2241

-0.00

-0.03

-0.04

0.6384

0.3159

0.2242

0.6382

0.3158

0.2242

-0.03

-0.03

0.00

0.6384

0.3159

0.2242

0.6384

0.3158

0.2242

0.00

-0.03

0.00

51
Table 7 (cont.)

50 Hz

10 Hz

1 Hz

0.1 Hz

50 Hz

10 Hz

1 Hz

0.1 Hz

NBS AC Voltage Calibrator

(millivolts)

LF Sampling

Voltmeter

(millivolts)

63.85

31.58

22.42

Error

% of reading

63.840

31.590

22.420

+0.016

-0.03

0.00

63.840

31.590

22.420

63.83

31.58

22.43

-0.015

-0.03

+0.04

63.840

31.590

22.420

63.84

31.58

22.42

0.00

-0.03

0.00

63.840

31.590

22.420

63.84

31.60

22.44

0.00

+0.03

+0.089

6.381

3.159

2.242

6.378

3.158

2.243

-0.05

-0.03

+0.04

6.390

3.162

2.241

6.388

3.160

2.241

-0.03

-0.06

0.00

6.391

3.162

2.241

6.389

3.160

2.241

-0.03

-0.06

0.00

6.384

3.159

2.241

6.383

3.158

2.241

-0.015

-0.03

0.00

52
Figures 13, 14, 15, and 16 are plots of the above error data for the

10 V, 1 V, 100 mV, and 10 mV ranges, respectively. These data show

evidence that the preamplifier does not add significant rms measurement

errors to the basic design and that these instruments can meet the

±0.1 percent of reading accuracy specification.

6.3 Harmonic Distortion Tests

The high stability sine wave generator discussed in section 6.2

was used to check the total harmonic distortion (THD) measurement

algorithm. This function and the associated algorithm is described

in section 2.2.4 under Theory of Operation. By reprogramming the

contents of the ROM used in the aforementioned sine wave generator, a distorted sine waveform with known ac offset and 4.7 percent of third

harmonic distortion was used to test the distortion function (see

fig. 17). The THD was measured for many values of voltage and

frequency and was found to be within 4.7 ±0.1 percent, except at

frequencies >80 Hz where the filter on the waveform generator began

to attenuate the third harmonic. Compensating for the reduced third

harmonic produced by the generator above 80 Hz yielded results in

agreement with the measurements.

7. CONCLUSIONS

The means for the accurate measurement of accelerometer-amplifier

outputs and other low-frequency vibration transducers using a sampling

technique have been developed. These methods have been embodied in a true rms ac voltmeter and distortion analyzer that has been shown to

have a measurement accuracy to ±0.1 percent (of reading) of the

fundamental frequency, total harmonic distortion, and true rms voltage

of approximately sinusoidal inputs from 2 mV to 10 V and frequencies

from 0.1 to 120 Hz.

A microcomputer is utilized for implementing special measurement

algorithms and timing and control functions, together with a conventional S/H amplifier and successive approximation type A/D

converter (data acquisition module) for digitizing the input signal.

By obtaining first an approximate (~1 percent) measure of the

signal period with a purely software window crossing technique, a more exact determination of period can then be calculated with an autocorrelation function that consists of summing the difference in

the values of samples taken at approximately corresponding times on the waveform cycle. It is shown that, assuming there are no other

errors, the accuracy required for the period measurement is one half

the accuracy required for the rms value. In the prototype voltmeter,

the approximate period is determined in the first cycle and the

exact period is then determined from the data samples taken during

the second cycle of the input signal.

53
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57
Figure 17. An example of a distorted sine

harmonic distortion) with a dc

waveform generator.

wave (4.7 percent third

offset produced by the

58
Using the mathematical definition of the rms value of a periodic

waveform, the rms value (of both the ac plus dc components and the ac only component) of the signal is obtained from the sample set of the

second cycle using numerical (midpoint) integration. When the exact

period does not contain an integral number of samples, a small end

correction is applied.

With nominally 128 samples taken over one period, a 64-point

decimation-in-time FFT is computed to obtain the dc, fundamental, and

30 harmonic component coefficients of the input signal. The THD

figure-of-merit is then calculated by squaring and summing the

coefficients of the 30 harmonics and dividing this sum by the sum

of the squares of the harmonic plus the fundamental.

An analysis of the sources of measurement errors and tests of the

frequency (period), rms value, and harmonic distortion functions of

the voltmeter have shown that the principles developed and employed

in the LF Sampling Voltmeter described herein are a significant

improvement over previously available means.

59
8. REFERENCES

[I] F. L. Hermach, AC-DC Transfer Instruments for Current and Voltage

Measurements, IRE Trans, on Instr., Vol. 1-7, Nos. 3 and 4,

Dec. 1958.

[2] E. S. Williams, Thermal Voltage Converters and Comparators for

\lery Accurate AC Voltage Measurements, Nat. Bur. Stand. (U.S.),

J. Res., Vol. 75C, Nos. 3 and 4, Dec. 1971.

[3] F. L. Hermach, AC-DC Comparators for Audio-Frequency Current and

Voltage Measurements of High Accuracy, IEEE Trans, on Instr. and

Meas., Vol. IM-25, No. 4, Dec. 1976.

[4] H. K. Schoenwetter, An RMS Digital Voltmeter/Calibrator for

Very Low Frequencies, IEEE Trans, on Instr. and Meas., Vol. IM-27,

No. 3, Sept. 1978.

[5] H. K. Schoenwetter, NBS Provides Calibration Service in 0.1-10 Hz

Range Using AC Voltmeter/Calibrator, Proceedings of EEMTIC '79,

Ottawa, Ontario, May 15-17, 1979.

[6] B. F. Field, A Fast Response Low Frequency Voltmeter, IEEE

Trans, on Instr. and Meas., Vol. IM-27, No. 4, Dec. 1978.

[7] R. S. Koyanagi, Development of a Low Frequency Vibration Calibration

System, Nat. Bur. Stand. (U.S), NBS Report 10529, Jan. 1971.

[8] R. S. Koyanagi and J. D. Pollard, Piezoelectric Accel erometer

Low-Frequency Response by Signal Insertion Methods, Nat. Bur. Stand.

(U.S.), NBS Report 74-597, May 1975.

[9] J. W. Cooley and J. W. Tukey, An Algorithm for the Machine

Computation of Complex Fourier Series, Math. Comp., Vol. 19,

pp. 297-301, Apr. 1965.

[10] G. D. Bergland, A Guided Tour of the Fast Fourier Transform,

IEEE Spectrum, Vol. 6, pp. 41-52, July 1969.

[II] B. F. Field, A Sampling Approach to the Measurement of Low Frequency

Voltage Waveforms, Ph.D. Thesis, Univ. of Md., Dept. of EE,

Dec. 8, 1978.

[12] C. K. Kostopoulos, Computing the Square Root of Binary Numbers,

Computer Design, pp. 53-57, Aug. 1972.

[13] S. A. Tretter, Introduction to Discrete-Time Signal Processing,

John Wiley & Sons, Inc., New York, 1976.

60
[14] S. K. Tewksbury, et al., Terminology Related to the Performance

of S/H, A/D, and D/A Circuits, IEEE Trans, on Circuits and Systems,

Vol. CAS-25, No. 7, July 1978.

[15] B. M. Gordon, Design Reference Guide, The Analogic Data-Conversion

Systems Digest, Edition 2, 1977.

[16] S. D. Stearns, Digital Signal Analysis, Hayden Book Company, Inc.,

New Jersey, 1975.

[17] T. M. Souders, D. R. Flach, and B. A. Bell, A Calibration Service

for Analog-to-Digital and Digital-to-Analog Converters, Nat. Bur.

Stand. (U.S.), Tech. Note 1145, July 1981.

61
APPENDIX A - CALIBRATION PROCEDURES

A.l .1 Setup

Calibration of the voltmeter should be performed in the order given

here and in the following sectionsJ Equipment needed will be a microvolt null detector (with at least a 3 mV full-scale deflection)

and an accurate (at least 0.1 percent) ac rms source with the

capability of outputting between 10 mV-10 V rms at a frequency of

5 Hz-10 Hz. First, remove the front panel retaining screws and,

secondly, situate the front panel so as to have access to both the

preamp backplate (where all trim pots are located) and the front

panel pushbuttons. Be careful not to short the display board against

either the instrument case or the backplane of the card cage. The

most convenient position for the front panel is to swing it out from

the preamp side as far as connection wires will allow, and tilt the

top of the front panel about 30° from the vertical. A portable vise

is handy to hold it in this position. Also, the bottom plate should

be removed to have access to the preamp coaxial cable end. Once

this is done, proceed to sections A. 1.2 and A. 1.3 on balance and

gain adjustments. If offset has already been adjusted, proceed

directly to section A. 1.3 regarding gain adjustment.

A. 1.2 Balance Adjustment

This procedure simultaneously adjusts for preamplifier offset, bias

current, and power supply effects. The first step in the procedure

is to short the HIGH-LOW input terminals to the GND terminal. Then

connect the BNC output of the preamp to the null detector with the

null detector set to a less sensitive range. Turn on the voltmeter

power switch. Depress and hold the front panel 10 mV pushbutton if

the instrument is not on that range setting. Adjust the output offset

using the pot label "BAL" on the preamp backplate until a null is

obtained. It might be appropriate at this time to increase the null

detector sensitivity to be certain that a null has been reached.

Next, once this null has been established, decrease the null detector

sensitivity, release the 10 mV pushbutton, and depress and hold the

1 V pushbutton. Adjust the pot labeled "NULL" to achieve a new null.

Again, increase null meter sensitivity to verify that a null has been

reached, then decrease the sensitivity. Release the 1 V pushbutton and

depress the 10 mV pushbutton. Readjust BAL for a new null. Depress

and hold the 1 V pushbutton. Readjust NULL for a new null. Repeat

this process until the desired null (less than a millivolt) is achieved,

iThis procedure assumes that the gain adjustments of the data

acquisition channel (S/H amplifier and A/D converter) are properly set

to make accurate dc voltage measurements on its 2.5, 5, and 10 V ranges

62
A. 1.3 Gain Adjustment

The source referred to here is the accurate ac rms source mentioned in

section A. 1.1. A frequency of approximately 5-10 Hz should be available.

The actual value is not important and these numbers are chosen to

facilitate good low-frequency calibration and to speed up the calibration

process. With this instrument the 1 V range should always be adjusted

first since it impacts all other ranges. Connect the ac source to

the HIGH and LOW terminals, and adjust the source to 500 mV rms. If

the instrument is working correctly, a number should appear on the

front panel numerical display. Depress and hold, if necessary, the 1 V

pushbutton. Adjust "1 V" pot on the preamp backplate until 500 mV

appears on the front panel display. It is important to note at this

time that since the instrument is averaging data before displaying

the results, the immediate effects of turning any gain pot will not

be noticed right away. Release the 1 V pushbutton. Adjust the source to 50 mV rms. Depress and hold, if necessary, the 100 mV

pushbutton. Trim the pot labeled "100 mV" on the preamp backplate

until 50 mV is indicated on the front panel display. Release the

100 mV pushbutton. Adjust the source to 5 mV rms. Depress and

hold, if necessary, the 10 mV pushbutton. Trim the pot labeled "10 mV"

on the preamp backplate until 5 mV is indicated on the front panel

display. Release the 10 mV pushbutton. Adjust the source to 5 V rms. Trim the pot labeled "10 V" on the preamp backplate until 5 V is

indicated on the front panel display. Calibration of the instrument

is now complete.

63
APPENDIX A - CALIBRATION PROCEDURES

A.l .1 Setup

Calibration of the voltmeter should be performed in the order given

here and in the following sections, 1 Equipment needed will be a microvolt null detector (with at least a 3 mV full-scale deflection)

and an accurate (at least 0.1 percent) ac rms source with the

capability of outputting between 10 mV-10 V rms at a frequency of

5 Hz-10 Hz. First, remove the front panel retaining screws and,

secondly, situate the front panel so as to have access to both the

preamp backplate (where all trim pots are located) and the front

panel pushbuttons. Be careful not to short the display board against

either the instrument case or the backplane of the card cage. The

most convenient position for the front panel is to swing it out from

the preamp side as far as connection wires will allow, and tilt the

top of the front panel about 30° from the vertical. A portable vise

is handy to hold it in this position. Also, the bottom plate should

be removed to have access to the preamp coaxial cable end. Once

this is done, proceed to sections A. 1.2 and A. 1.3 on balance and

gain adjustments. If offset has already been adjusted, proceed

directly to section A.l .3 regarding gain adjustment.

A. 1.2 Balance Adjustment

This procedure simultaneously adjusts for preamplifier offset, bias

current, and power supply effects. The first step in the procedure

is to short the HIGH-LOW input terminals to the GND terminal. Then

connect the BNC output of the preamp to the null detector with the

null detector set to a less sensitive range. Turn on the voltmeter

power switch. Depress and hold the front panel 10 mV pushbutton if

the instrument is not on that range setting. Adjust the output offset

using the pot label "BAL" on the preamp backplate until a null is

obtained. It might be appropriate at this time to increase the null

detector sensitivity to be certain that a null has been reached.

Next, once this null has been established, decrease the null detector

sensitivity, release the 10 mV pushbutton, and depress and hold the

1 V pushbutton. Adjust the pot labeled "NULL" to achieve a new null.

Again, increase null meter sensitivity to verify that a null has been

reached, then decrease the sensitivity. Release the 1 V pushbutton and

depress the 10 mV pushbutton. Readjust BAL for a new null. Depress

and hold the 1 V pushbutton. Readjust NULL for a new null. Repeat

this process until the desired null (less than a millivolt) is achieved,

iThis procedure assumes that the gain adjustments of the data

acquisition channel (S/H amplifier and A/D converter) are properly set

to make accurate dc voltage measurements on its 2.5, 5, and 10 V ranges

62
A. 1.3 Gain Adjustment

The source referred to here is the accurate ac rms source mentioned in

section A. 1.1. A frequency of approximately 5-10 Hz should be available.

The actual value is not important and these numbers are chosen to

facilitate good low-frequency calibration and to speed up the calibration

process. With this instrument the 1 V range should always be adjusted

first since it impacts all other ranges. Connect the ac source to

the HIGH and LOW terminals, and adjust the source to 500 mV rms. If

the instrument is working correctly, a number should appear on the

front panel numerical display. Depress and hold, if necessary, the 1 V

pushbutton. Adjust "1 V" pot on the preamp backplate until 500 mV

appears on the front panel display. It is important to note at this

time that since the instrument is averaging data before displaying

the results, the immediate effects of turning any gain pot will not

be noticed right away. Release the 1 V pushbutton. Adjust the source to 50 mV rms. Depress and hold, if necessary, the 100 mV

pushbutton. Trim the pot labeled "100 mV" on the preamp backplate

until 50 mV is indicated on the front panel display. Release the

100 mV pushbutton. Adjust the source to 5 mV rms. Depress and

hold, if necessary, the 10 mV pushbutton. Trim the pot labeled "10 mV"

on the preamp backplate until 5 mV is indicated on the front panel

display. Release the 10 mV pushbutton. Adjust the source to 5 V rms. Trim the pot labeled "10 V" on the preamp backplate until 5 V is

indicated on the front panel display. Calibration of the instrument

is now complete.

63
APPENDIX B - MAINTENANCE AND TROUBLESHOOTING

A. 2 Maintenance

The following portion of this manual contains information and procedures

designed to aid in the troubleshooting and repair of the Low-Frequency

Sampling Voltmeter. Each section is titled by a specific fault

possibility with information given on the probable cures.

A. 2.1 No power

In the event that the front panel LEDs, numerical display, and back

panel fan are not operating, turn off power, check the fuse in the

fuse holder on the back panel and replace with a 125 V, 5 A fuse.

Before turning power back on, check all the internal power lines in

the instrument (yellow, orange, red) for possible shorts. All the

power supply outputs are currently protected against shorts, but

power failure has been known to occur if different supply outputs are connected together.

A. 2. 2 Front panel numerical display is functioning; no LEDs are turning on

Turn off power. Check the +12 V line from the Kepco power supply

(orange lead). This line runs from the power supply to the backplane

connector 03 pin 52, to pin 9 of the 50 pin ribbon connector, to the

front panel display board. Make sure the 50 pin connector is secure

at both ends. Check the integrity of the +12 V path and, if okay, remove the front panel display board from the front panel with all

connectors to this board intact (connector to preamp, switches, and

50 pin connector). Be careful not to short the display board against

the case, the backplane, or the front panel. Turn on the power. The

LEDs should now work, indicating that a short existed between the

display board and the front panel. Turn off the power. Reassemble

the instrument, and correct the shorting condition. If the LEDs still

do not work, the +12 V supply has probably failed.

A. 2. 3 Erratic behavior of the LEDs

Push the reset button. If there are still improper results, turn the

power off momentarily, then switch power back on. If this procedure

fails, remove the front panel display board connector from the pushbutton

switches, and examine for loose connections. Also, check to see that the 50 pin connector is secure on both ends, and that all printed

circuit boards are secure in their respective card cage connectors.

64
A. 2.4 Reset not functioning

Refer to section A. 2. 3. If this procedure fails, check the wirewrap

connection on the card cage backplane - pin 56 of J3 to pin 15 of Jl.

If this path is okay, then an integrated circuit failure exists on the memory, timing, and control I/O board (probably IC20).

A. 2. 5 LEDs functioning; no front panel numerical display

Check the +15 V, -15 V and analog ground lines (red, yellow, green)

on the terminal strip located on the backplane of the card cage on the

side furthest from the Kepco power supply. Push reset and make sure that the overload indicator is not ON. If it is, then the incoming

signal exceeds the limits of the instrument's measuring capability.

Check the BNC connection to the A/D converter board from the preamp.

Make sure that the A/D converter board is secure in card cage connector

J3. If the problem persists after this check, the trouble is probably

in the preamp; go to appendix A for calibration.

A. 2. 6 Erratic detection of the incoming signal

Make sure all printed circuit boards are secure in their respective

card cage connector, and check that the 50-pin ribbon connector is secure on both ends. Perform the checks designated in section A. 2. 5.

If the problem still exists after these checks, it is probably an integrated circuit failure problem on the memory, timing, and control

I/O board. Replace IC's 8, 7, 6, and 5 (sampling rate generator) on the memory, timing, and control I/O board.

A. 2. 7 No response to pushbutton selections; functioning otherwise

Perform the checks designated in section A. 2. 3.

A. 2. 8 No range, mV, or volt LEDs activated, but instrument is working

The instrument has just recovered from an overload; push 10 mV range

button to restore LEDs.

A. 2. 9 Improper values being displayed on numerical display; otherwise

instrument working

Turn to calibration, appendix A. Perform the necessary procedure.

If the problem persists, the number displayed is an overload on that

particular range. To correct, push next higher range button. If the

problem still exists, refer to section A. 2. 6 above.

65
APPENDIX C - SCHEMATICS

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71
APPENDIX D - PHOTOGRAPHS

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APPENDIX E - PARTS LIST

NBS 722 791 84A Preamplifier Board

Description

1. Analog Devices 606J amplifier

2. Teledyne TP319 operational amplifier

3. 1/4 Watt Vishay resistors

66,5 kn

5690 n 100 kn

500 Q

2 kfi 499 n 82 fi

4. Helitrim pots (pc board type)

5 k

500 Q

2 k 100 k 10 k

5. Miniature chokes 2 yh, 1/4 watt

6. 10 yf, 35 V (polarized) Tantalum capacitor

7. Resistors 10%, 1/4 watt. Tin oxide

200 n

5.1 k

8 k

Identification

Quantity Nc)(s)

1 E

1 F

1 R12

1 R7

2 Rl, R2

1 RIO

3 R4, R5, R13

1 R8

1 Rll

1 RV4

1 RV3

1 RV2

1 RV5

2 RVl,, RV6

2 LI, L2

2 CI. C2

1 R9

1 R3

1 R14

80
PARTS LIST

NBS 722 79184A Preamplifier Board (cont.)

Description Quantity

Identification

No(s)

8. Resistors 1%, 1/4 watt

1 m

100 kQ

9. Coto-Coil Relays, CR-3702-12

CR-3206-12 II II

R6

R15, R16

A, C, D

B

81
PARTS LIST

Preamp Board (cont.)

Miscellaneous List

Description Quantity

1. 3M No. 3406 connector 2

2. 4" flat 14 conductor ribbon cable 1

3. 1/8" MU-METAL box for preamp housing

Body 4 7/8" x 4 1/8" x 1 1/8" 1

Lid 4 3/4" X 4" x 1 1/8" 1

4. Bendix 3022-12 BNC connector 1

5. 14" RF-174/U shield cable 1

6. Red & Black dual female banana receptacle

chassis mount

7. Black single banana receptacle chassis mount 1

8. 14 pin low profile dip socket 1

9. 1/2" 6-32 threaded steel spacer 2

10. 1/4" 6-32 threaded steel spacer 4

11

6-32 steel nuts 4

12. 1/2" flat head steel screw 2

13. 3/4" flat head steel screw 2

14. Nylon washer 0.196 ID 6

15. Nylon nut 6-32 2

82
1. 9374

2. 7442

3. 74175

4. 74138

5. 74174

6. 74123

7. 7406

8. 7400

Identification

Quant"ity No(s)

4 2, 3, 4, 5

1 7 2 6, 15

1 8

2 10, 11

1 14

3 12, 13, 16

1 9

PARTS LIST

NBS 7279026A Display Board

Description

I. INTEGRATED CIRCUITS

LED digit driver

BCD to DECIMAL decoder

(or 74LS175) Quad D-type flip flop

(or 74LS138) 3- to -8 Line decoder

(or 74LS174) Hex D-type flip flop

Dual One-Shot with clear

30 V Hex inverter/driver

7400 (or 74LS00) Quad 2 input NAND gate

II. LEDS

1. MAN 6660 LED Numerical display 4 DS2 - DS5

2. LITRONIX RED-LIT-C201 (or equivalent) 14 LEDl - LED 13

III. RESISTORS and CAPACITORS

1. 2 kn, 10%, 1/4 W Composition resistor

2. 15 k^, 10%, 1/4 W Composition resistor

3. 1 kQ, 10%, 1/4 W Composition resistor

4. 30. , 1%, 5 W Composition resistor

5. 51 9,, 10%, 1/4 Composition resistor

6. 100 pF, 100 V, Dipped mica capacitor

7. 10 yf, 35 V (polarized) Tantalum capacitor

8. 500 pF, 100 V, Dipped mica capacitor

9. 0.1 uf, 50 V, Monolithic ceramic capacitor

IV. MISCELLANEOUS

1. 14 pin Low profile dip socket 1 DIP 1 2. 14 pin connector S ribbon cable, 3M #3406

(or equiv.) 1 3. 50 pin 90° ribbon connector (3M or equiv.) 1 4. 16 pin (wire wrap) Low profile dip socket 1 DIP 2

1 Rl

1 R2

1 R3

T R4

4 R5, R6, R7, R8

1 CI

2 C2, C5

1 C3

1 C4

83
PARTS LIST

NBS 722 79094A Memory I/O Board

Description

1. INTEGRATED CIRCUITS

1 . 2k X 8 2716 EPROMS

2. 74150 Data selector/multiplexer

3. 74157 Quad 2 to 1 data selector

4. 74157 Quad 2 to 1 data selector (optical)

5. 74174 Hex D-type flip-flop

6. DM8095 Tri-state buffer and latch

7. 7475 (or 74LS75) Quad bistable latch

8. 74191 (or 74LQ191) up/down binary counter

9. 7493 (or 74LS93) 4-bit binary counter

10. 7474 (or 74LS74) dual D-type flip flop

11. 74175 (or 74LS175) Quad D-type flip flop

12. 7400 (or 74LS00) Quad 2 input NAND gate

13. 7402 (or 74LS02) Quad 2 input NOR gate

14. 7485 (or 74LS85) 4-bit magnitude comparator

15. 7406 30 V Hex inverter/driver

16. 74121 Monostable multivibrator

II. RESISTORS and CAPACITORS

lA. 5.1 kn, 10%, 1/4 W, composition resistor

IB. 5.1 kn, 1%, 1/4 W, composition resistor

2. 10 k^, 10%, 1/4 W, composition resistor

3. 100 kn, 10%, 1/4 W, composition resistor

4. 10 or 22 yf, 35 V (polarized) Tantalum

capacitor

5. 0.1 yf, 50 V, monolithic ceramic capacitor

6. 0.01 yf, 50 V, monolithic ceramic capacitor

III. MISCELLANEOUS

1. 24 pin I.e. socket (Cambion or equiv.)

for item I.l

.

2 2. 50 pin 90° ribbon connector (3M or equiv.) 1 3. Card ejector clip (Cambion or equiv.) 2 4. #2-56, 3/4" machine screw 2

Identification

Quantity No(s)

2 29, 30

1 12

2 32, 33

(1) 31

3 13, 14, 15

3 25, 26, 27

4 1, 2, 3, 4

4 5, 6, 7, 8

3 9, 10, 11

1 17

1 21 4 19, 20, 22, 28

1 16

1 34

1 24

2 18, 23

1 R4

1 Rl

1 R2

1 R3

2 C5, C7

1 C2

5 CI, C3, C4, C6, C8

84
PARTS LIST

NBS 722 79141A A/D Board

Identification

Description Quantity No(s)

1. Data Model MDAS-8D 1 data acquisition module and 3-36063-2

72 pin AMP connector

2. 1N485B switching diodes (or equiv.) 3 Dl , D2, D3

3. 191TE2A1-5G SIGMA reed relays (or equiv.) 3 A, B, C

4. 0.01 uf, 50 V, monolithic ceramic capacitor 4 CI, 3, 5, 7

5. 10 yf, 35 V (polarized) Tantalum capacitor 4 C2, 4, 6, 8

6. LEMO size chassis mount coax connector 1

7. RG178 coax cable (~3" long) 1

8. Card ejector clip (Cambion or equiv.) 2

9. 1/4" 4-40 screws 2

85
INSTRUMENT PARTS LIST

Quantity

1. CPU Board National Semiconductor IMP-16C/3000A

2. I/O Memory Board NBS 722 79094B (see detailed parts list)

3. A/D Board NBS 722 79141A

4. Display Board NBS 722 79026A

5. Preamplifier Board NBS 722 79184A

6. Card Cage National Semiconductor IMP-OOH/880

7. Kepco Power Supply RMT-001-AA

+12 V at 1 A

-12 V at 1 A

+5 V at 10 A

8. Analog Devices Dual Power Supply 9021

±15 V DC/100 mA (115 V option)

9. 24" 50 conductor flat ribbon cable with 3M No. 3425

50 pin female connectors at each end

10. ROTRON whisper fan WR2A1 , 115 V 11. ROTRON #551147 finger guard

12. CORCOM line filter and fuse holder

13. Fuse, 125 V, 5 A

14. Switchcraft all lock 65043-206 switches

15. Switchcraft interlock 65041K-206 switches

16. Plexiglas, dark ruby, 4" x 1 1/2"

17. Wiring set from Kepco supply to card cage (see schematic)

18. Wiring set from Analog supply to card cage " 19. Cable from Analog supply to preamp

" 20. Terminal strips, 4 conductor type

21. NBS LF AC Voltmeter, 19" x 4 3/4" front panel for #19 rack

22. Side panel, 13" x 3 1/8"

23. Back panel, 17" x 5 1/4"

24. Top lid

25. Bottom lid

26. Socket for item #8 Analog Devices AC-1040

27. Switch wiring cable to display board (see schematic)

28. Supporting bracket from side panels to front panel

29. Fan power cord for item #10

30. Double pole single throw switch (5 A at 125 V)

86
Miscellaneous Hardware

1. Mounting hardware for fan

flat head 3/4" steel 6-32 screw 4

6-32 steel nut 4

2. Mounting hardware for 9021 power supply

6-32 1/4" steel screw 4

6-32 1/2" steel screw 4

1/2" thread 6-32 steel spacer 4

3. Mounting hardware for card cage

angle iron 1", 1/2", 1/8" thickness 2 8/32 steel screws 1/2" 2 6/32 steel screws 3/4" 6

6/32 steel nut 9

steel washer 0.19610 2

4. Iron mesh, 7" x 5" 1 6/32 1" steel screw 4

6/32 steel nut 4

retaining washer 4

5. Mounting hardware for front panel

6/32 1" flat head steel screw 4

steel spacer 1/4" 6-32 threaded 8

insulating washer 0,196 ID 8

nylon nut, 6-32 8

6. Side panel to front panel

8-32 flat head 1/2" steel screw 4

7. Bracket hardware (item #28 on instrument parts list)

8-32 1/4" steel screw 2

8-32 1/2" steel screw 3

8-32 steel nut 3

8. Side panel to back panel

8-32 1/2" steel screw 2

9. Top lid hardware

6-32 1/4" steel screw 4

10. Bottom lid hardware

6-32 1/4" steel screw 4

11. Mounting hardware for switches

4-40 1/4" steel screw 5

87
APPENDIX F - FLOWCHARTS OF CERTAIN MAJOR SUBROUTINES

FROM PAGE 89 &

INCREMENT WINDOW LENGTH COUNTER

f PERIOD

j

SET CLK TO

500 Hz

T

INITIALIZE WINDOW

COUNTERS

TAKE READING

(JSR WAIT)

INITIALIZE WINDOW

PARAMETERS 3TAKE READING

(JSR WAIT)

APPROXIMATE PERIOD

ROUTINE

FROM

PAGE 89 ©

CH REDUCE

PREAMP GAIN 6

SET PREAMP

GAIN TO

MINIMUM

TO PAGE 89

88
FIND WINDOW

(JSR TSTKH)

FIND WINDOW

(JSR TSTKH)

FROM

PAGE 88 iSTORE WINDOW LIMITS

APPROXIMATE PERIOD

(CONTINUED)

ADJUST WINDOW

TO START AT PEAK ADJUST WINDOW LENGTH ACCORDINGLY

STORE WINDOW LENGTH

C 1 TO PAGE 90

TO PAGE 88 89
FROM

PAGE 89 fCALCULATE CORRECTION FOR

CLK FOR A SAMPLE RATE

126 X fo

w

SET CLK TO NEW FREQUENCY

1 r

( RETURN j

APPROXIMATE PERIOD

(CONTINUED)

90
SUBROUTINE IN APPROXIMATE

PERIOD TO FIND WINDOW

(LOW FREQUENCY < 5 HZ)

MORE THAN 3000 SAMPLES TAKEN WITHOUT FINDING WINDOW, RETURN TO PROGRAM START

INCREMENT COUNTER
( TSTKH

J

SUBROUTINE IN APPROXIMATE

PERIOD TO FIND WINDOW

(HIGH FREQUENCY > 5 HZ)

3TAKE

READING

(JSR WAIT)

MORE THAN

3000 SAMPLES TAKEN WITHOUT

FINDING WINDOW

RETURN TO START

INITIALIZE TEST REGISTERS <)

STORE MINIMUM OR MAXIMUM

INCREMENT COUNTER

92
( XPER

J EXACT PERIOD ROUTINE

INITIALIZE REGISTER DELTA

CALCULATE ERROR VALUE

(JSR ERRSUM)

INITIALIZE MINIMUM ERROR

VALUE

DECREMENT

DELTA

CALCULATE I

ERROR VALUE

(JSR ERRSUMI

YES

ORDER READINGS AND STORE

JUMP TO ERROR

SUBROUTINE

(JSR ERROR)

DECREMENT

DELTA

JUMP TO ERROR

SUBROUTINE

(JSR ERROR)

TO PAGE 94

93
FROM

PAGE 93

REORDER iFOUR

POINTS NEAREST

MINIMUM. PUT IN PREDETERMINED ORDER

INTERPOLATE TO FIND DELTA

AT ERROR

VALUE

MINIMUM.

( RETURN

j

EXACT PERIOD (CONTINUED)

c \

I ERRSUM I

INITIALIZE REGISTERS

I = 16

SUBROUTINE FOR

EXACT PERIOD

COMPUTE

V

i - V i , DELTA

TAKE ABSOLUTE

VALUE, SUM

INTO REGISTER

JUMP TO ERROR

SUBROUTINE

(JSR ERROR)

94
( AVEG

J ROUTINE TO AVERAGE

RMS READINGS

MOVE STORED

READINGS BACK ONE LOCATION

IN STACK

STORE NEW

READING AT THE TOP OF

THE STACK

INCREMENT NRDG

COMPUTE NEW

AVERAGE FROM

READINGS IN STACK

{ RETURN

J

95
SHIFT ANSWER

LEFT ONE

BIT

( SORT j

INITIALIZE REGISTERS: COUNTER ° 32 5ADD 01 TO ANSWER

SHIFT INPUT

LEFT INTO WORKING

REGISTER

SUBTRACT ANSWER FROM

WORKING

REGISTER

STORE RESULT

IN WORKING

REGISTER

SHIFT5ANSWER

LEFT ONE

BIT

SUBROUTINE FOR SQUARE ROOT

YES MOVE ANSWER

TO ACCUMULATORS

C

' N f RETURN 1

96
( DIST

j DISTORTION ROUTINE

COMPUTE

DFT USING SUBROUTINE

FFT

CALCULATE MAGNITUDE OF FUNDAMENTAL

CALCULATE MAGNITUDE

OF HARMONICS

STORE IN SUM2

ADD HARMONICS

TO FUNDAMENTAL

STORE IN SUM

NORMALIZE SUM, SUM 2 FOR

FIXED POINT

DIVIDE

DIVIDE SUM 2

(32 bits) BY SUM (16 bits) 32 bit RESULT

TAKE SQUARE ROOT OF RESULT

(JSR SORT)

©TO PAGE 98

97
FROM PAGE 97 iMULTIPLY RESULT BY 100 TO EXPRESS IT IN PERCENT

DISPLAY RESULT (THD)

(JSR DISP)

DISTORTION ROUTINE

(CONTINUED)

RESET SAMPLE

RATE CLOCK

TO 128 X INPUT FREQUENCY

I

( RETURN

J

98
c

FFT 1

i

INITIALIZE REGISTERS

SET 1 = 32

LOAD5A(l), B(l) DO FFT BUTTERFLY

CALC. (Wo = 1)

FAST FOURER TRANSFORM

SUBROUTINE

(PART OF DISTORTION ROUTINE)

JUMP TO

OVERFL SUBROUTINE

END OF FIRST PASS

MGF = 2 PN .1 (or PN > 2

for PN i 2

^Q ^ 2 (MPN - PN)

MPN = MAX. PASS NUMBER - 6

TO PAGE 100

99
INCREMENT LOOP COUNTERS

GF

FROM

PAGE 99 i

FAST FOURER TRANSFORM

(CONTINUED)

INITIALIZE GROUP FACTOR

(GF = O)

SET K OF W K FROM TABLE

LOOKUP TWIDDLE FACTOR

(JSR WNK)

INITIALIZE LOOP COUNTER M

(M = NG)

DO5BUTTERFLY CALCULATION

(JSR BUTFLY)

NORMAL

RETURN

OVERFLOW RETURN JUMP TO OVERFLOW

SUBROUTINE

INCREMENT

INPUT LOCATION COUNTERS

INCREASE INPUT COUNTERS TO

PROPER VALUE

TO PAGE 101

100
FAST FOURIER TRANSFORM

(CONTINUED)

I RETURN j

TO PAGE 99

INCREMENT LOOP COUNTER

PN

RESULTS ARE RETURNED IN ORIGINAL ARRAY IN BIT REVERSED ORDER

101
f BUTFLY

J BUTTERFLY SUBROUTINE

FOR FFT

LOAD IMAG PART

OF B AND IMAG

PART OF W

MULTIPLY

(32 bit result)

STORE RESULT

IN TEMPORARY

LOCATION

LOAD REAL PART OF B AND REAL PART OF W

MULTIPLY

(32 bit result)

SUBTRACT

RESULT FROM

FIRST PRODUCT

ROUND ANSWER

TO 16 bits, AND, STORE IN TEMP'

ADD TEMP' TO REAL PART OF A

J OVERFLOW A \ RETURN J

STORE RESULT

IN TEMPORARY

LOCATION

SUBTRACT REAL PART OF A FROM TEMP' 1

102
BUTTERFLY SUBROUTINE

(CONTINUED)

< OVERFLOW ^

RETURN J

STORE RESULT

IN TEMPORARY

LOCATION

LOAD REAL PART OF B AND IMAG PART OF W

MULTIPLY

(32 bits result)

STORE RESULT

IN TEMPORARY

LOCATION

LOAD IMAG PART

OF B AND REAL PART OF W

MULTIPLY

(32 bit result)

SUBTRACT

RESULT FROM

PREVIOUS PRODUCT

ROUND ANSWER

TO 16 bite AND

STORE IN TEMP'

ADD TEMP' TO

IMAG PART OF A

TEST X^ YES FOR OVERFLOW < OVERFLOW A

RETURN J

103
iSTORE RESULT

IN TEMPORARY

LOCATION

SUBTRACT IMAG PART OF A FROM TEMP'

BUTTERFLY SUBROUTINE

(CONTINUED)

< OVERFLOW ^

RETURN J

STORE ALL RESULTS BACK

IN ORIGINAL ARRAY

I

( RETURN 1

104
USING K (W '^

) CALCULATE

K MOD (161

LOOKUP TABLE ADDRESS OF

TWIDDLE FACTOR

K M0D(16)

LOAD TWIDDLE FACTOR FROM

TABLE (REAL + IMAG) INTO REGISTERS

SUBROUTINE WNK FOR

CALCULATING TWIDDLE

FACTORS

EXCHANGE

REAL * IMAG PARTS

SET SIGNS

STORE SIGNS AND TWIDDLE FACTOR IN MEMORY

>

I RETURN 1

105
( OVERFL j

'

INITIALIZE COUNTERS — T

SHIFT DATA

1 BIT RIGHT EXTEND SIGN

BIT

NO ^Xdecrement >s^

X,^ IF DONE >^

YES

\

'

INCREMENT OVERFLOW COUNTER

y

( RETURN j

OVERFLOW SUBROUTINE

106
NBS-n4A (REV. 2-8C) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBS TN 1159

2. Performing Organ. Report No, 3. Publication Date August 1982

4. TITLE AND SUBTITLE

A FAST RESPONSE, LOW-FREQUENCY SAMPLING VOLTMETER

5. AUTHOR(S)

Barry A. Bell, Bruce F. Field, and Thomas H. Kibalo

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

Sponsored in part by the

DC and Low Frequency Engineering Subgroup of the

Calibration Coordination Group (CCG) of the

Department of Defense.

10. SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A ZOO-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

A low- frequency voltmeter utilizing a sampling technique

implemented with microprocessor-based electronics has been

developed to perform as a true rms ac voltmeter and distortion

analyzer. The instrument makes measurements accurate to

±0.1 percent (of reading) of the fundamental frequency, total

harmonic distortion, and true rms voltage of approximately

sinusoidal inputs from 2 mV to 10 V and frequencies from 0.1 to

120 Hz. A major feature of this instrument is the special

window crossing and error function algorithms which provide a software means for completing a measurement within two signal

periods at frequencies below 10 Hz.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

algorithm; converter; distortion; microcomputer; rms value; sampling;

signal period.

13. AVAILABILITY

|X~1 Unlimited

I I For Official Distribution. Do Not Release to NTIS

[X~| Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D C

20402.

1^^ Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

113

15. Price

USCOMM-DC aO43-P80

fll U . S . GOVERNMENT PRINTING OFFICEi 19 8 2-360-997/2210







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